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Journal articles on the topic 'Vertical conformal vector field'

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Author: Grafiati

Published: 9 March 2023

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1

Manev, Mancho. "Yamabe Solitons on Conformal Almost-Contact Complex Riemannian Manifolds with Vertical Torse-Forming Vector Field." Axioms 12, no. 1 (January 1, 2023): 44. http://dx.doi.org/10.3390/axioms12010044.

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A Yamabe soliton is considered on an almost-contact complex Riemannian manifold (also known as an almost-contact B-metric manifold), which is obtained by a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. A case in which the potential is a torse-forming vector field of constant length on the vertical distribution determined by the Reeb vector field is studied. In this way, manifolds from one of the main classes of the studied manifolds are obtained. The same class contains the conformally equivalent manifolds of cosymplectic manifolds by the usual conformal transformation of the given B-metric. An explicit five-dimensional example of a Lie group is given, which is characterized in relation to the obtained results.

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2

Siddiqi, Mohd Danish, Ali Hussain Alkhaldi, Meraj Ali Khan, and Aliya Naaz Siddiqui. "Conformal η-Ricci Solitons on Riemannian Submersions under Canonical Variation." Axioms 11, no. 11 (October 27, 2022): 594. http://dx.doi.org/10.3390/axioms11110594.

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This research article endeavors to discuss the attributes of Riemannian submersions under the canonical variation in terms of the conformal η-Ricci soliton and gradient conformal η-Ricci soliton with a potential vector field ζ. Additionally, we estimate the various conditions for which the target manifold of Riemannian submersion under the canonical variation is a conformal η-Ricci soliton with a Killing vector field and a φ(Ric)-vector field. Moreover, we deduce the generalized Liouville equation for Riemannian submersion under the canonical variation satisfying by a last multiplier Ψ of the vertical potential vector field ζ and show that the base manifold of Riemanian submersion under canonical variation is an η Einstein for gradient conformal η-Ricci soliton with a scalar concircular field γ on base manifold. Finally, we illustrate an example of Riemannian submersions between Riemannian manifolds, which verify our results.

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3

Manev, Mancho. "Almost Riemann Solitons with Vertical Potential on Conformal Cosymplectic Contact Complex Riemannian Manifolds." Symmetry 15, no. 1 (December 30, 2022): 104. http://dx.doi.org/10.3390/sym15010104.

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Almost-Riemann solitons are introduced and studied on an almost contact complex Riemannian manifold, i.e., an almost-contact B-metric manifold, which is obtained from a cosymplectic manifold of the considered type by means of a contact conformal transformation of the Reeb vector field, its dual contact 1-form, the B-metric, and its associated B-metric. The potential of the studied soliton is assumed to be in the vertical distribution, i.e., it is collinear to the Reeb vector field. In this way, manifolds from the four main classes of the studied manifolds are obtained. The curvature properties of the resulting manifolds are derived. An explicit example of dimension five is constructed. The Bochner curvature tensor is used (for a dimension of at least seven) as a conformal invariant to obtain these properties and to construct an explicit example in relation to the obtained results.

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4

SOLEIMAN, A. "ENERGY β-CONFORMAL CHANGE IN FINSLER GEOMETRY." International Journal of Geometric Methods in Modern Physics 09, no. 04 (May 6, 2012): 1250029. http://dx.doi.org/10.1142/s0219887812500296.

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The present paper deals with an intrinsic generalization of the conformal change and energy β-change on a Finsler manifold (M.L.), namely the energy β-conformal change ([Formula: see text] with [Formula: see text]; [Formula: see text] being a concurrent π-vector field and σ(x) is a function on M). The relation between the two Barthel connections Γ and [Formula: see text], corresponding to this change, is found. This relation, together with the fact that the Cartan and the Barthel connections have the same horizontal and vertical projectors, enable us to study the energy β-conformal change of the fundamental linear connection in Finsler geometry: the Cartan connection, the Berwald connection, the Chern connection and the Hashiguchi connection. Moreover, the change of their curvature tensors is obtained. It should be pointed out that the present work is formulated in a prospective modern coordinate-free form.

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5

Tannukij, Lunchakorn, and Jae-Hyuk Oh. "Partially massless theory as a quantum gravity candidate." International Journal of Modern Physics A 36, no. 17 (June 2, 2021): 2150122. http://dx.doi.org/10.1142/s0217751x21501220.

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We study partially massless gravity theory (PM gravity theory) and suggest an alternative way to add higher order interaction vertices to the theory. Rather than introducing self-interaction vertices of the gravitational fields to the partially massless gravity action, we consider interactions with matter fields, since it is well known that addition of the self-interaction terms necessarily breaks the [Formula: see text] gauge symmetry that PM gravity theory enjoys. For the coupling with matter fields, we consider two different types of interaction vertices. The first one is given by an interaction Lagrangian density, [Formula: see text], where [Formula: see text] is the PM gravity field and [Formula: see text] is the stress-energy tensor of the matter fields. To retain the [Formula: see text] gauge symmetry, the matter fields also transform accordingly and it turns out that the transform must be nonlocal in this case. The second type of interaction is obtained by employing a gauge covariant derivative with the PM gravity field, where the PM gravity fields play a role of a gauge connection canceling the phase shift of the matter fields. We also study the actions and the equations of motion of the partially massless gravity fields. As expected, it shows 4 unitary degrees of freedom — 2 of them are traceless tensor modes and they are light-like fields and the other 2 are transverse vector modes and their dispersion relation changes as background space–time (de Sitter) evolutes. In the very early time, they are light-like but in the very late time, their velocities become a half of speed of light. The vector mode dispersion relation shows momentum-dependent behavior. In fact, the higher (lower) frequency modes show the faster (slower) velocity. We call this effect “conformal (or de Sitter) prism”. We suggest their quantization, compute Hamiltonians to present their exited quanta and construct their free propagators.

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6

Khan, Suhail, Amjad Mahmood, and Ahmad T. Ali. "Concircular vector fields for Kantowski–Sachs and Bianchi type-III spacetimes." International Journal of Geometric Methods in Modern Physics 15, no. 08 (June 22, 2018): 1850126. http://dx.doi.org/10.1142/s0219887818501268.

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This paper intends to obtain concircular vector fields (CVFs) of Kantowski–Sachs and Bianch type-III spacetimes. For this purpose, ten conformal Killing equations and their general solution in the form of conformal Killing vector fields (CKVFs) are derived along with their conformal factors. The obtained conformal Killing vector fields are then placed in Hessian equations to obtain the final form of concircular vector fields. The existence of concircular symmetry imposes restrictions on the metric functions. The conditions imposing restrictions on these metric functions are obtained as a set of integrability conditions. It is shown that Kantowski–Sachs and Bianchi type-III spacetimes admit four-, six-, or fifteen-dimensional concircular vector fields. It is established that for Einstein spaces, every conformal Killing vector field is a concircular vector field. Moreover, it is explored that every concircular vector field obtained here is also a conformal Ricci collineation.

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7

Klaycham, Karun, Chainarong Athisakul, and Somchai Chucheepsakul. "Nonlinear Response of Marine Riser with Large Displacement Excited by Top-End Vessel Motion using Penalty Method." International Journal of Structural Stability and Dynamics 20, no. 04 (March 24, 2020): 2050052. http://dx.doi.org/10.1142/s0219455420500522.

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A marine riser operated in a deep-water field could be substantially affected by large amounts of movement of the floating platform, which is more complicated and very challenging to analyze. This paper presents a mathematical model involving nonlinear dynamic response analysis of a marine riser caused by sways and heave motions at the top end, which are treated as the constraint conditions. The nonlinear equation of motion, arising from the nonlinearity of the ocean current and wave loadings, is derived and written in general matrix form using the finite element method. The excitation caused by platform movement is imposed on the riser system through the time-dependent constrained condition using the penalty method. The advantages of this method are that it is easily implemented on the nonlinear equation of motion and it requires no additional unknown variable, and thus consumes less computational time. By this method, the stiffness matrix and the force vector of the system are then modified, enforcing top-end vessel motion. The dynamic responses are evaluated by using numerical time integration based on Newmark’s method with direct iteration. The effects of the oscillation frequency of top-end vessel sway and heave motions on the nonlinear dynamic characteristics of the riser are investigated. The numerical results reveal that the riser responses to the top-end vessel excitation behave like a periodic motion, which is conformable to the characteristics of vessel movements. The increase in the oscillation frequency of the top-end vessel increases the maximum displacement amplitude for both the horizontal and vertical directions. The directional motion of the vessel also significantly influences the response amplitude of the riser.

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8

De, Uday Chand, Young Jin Suh, and Sudhakar K. Chaubey. "Conformal vector fields on almost co-Kähler manifolds." Mathematica Slovaca 71, no. 6 (December 1, 2021): 1545–52. http://dx.doi.org/10.1515/ms-2021-0070.

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Abstract In this paper, we characterize almost co-Kähler manifolds with a conformal vector field. It is proven that if an almost co-Kähler manifold has a conformal vector field that is collinear with the Reeb vector field, then the manifold is a K-almost co-Kähler manifold. It is also shown that if a (κ, μ)-almost co-Kähler manifold admits a Killing vector field V, then either the manifold is K-almost co-Kähler or the vector field V is an infinitesimal strict contact transformation, provided that the (1,1) tensor h remains invariant under the Killing vector field.

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9

MANOFF, S. "CONFORMAL DERIVATIVE AND CONFORMAL TRANSPORTS OVER $\bm{({\bar L}_n,g)}$-SPACES." International Journal of Modern Physics A 15, no. 05 (February 20, 2000): 679–95. http://dx.doi.org/10.1142/s0217751x00000343.

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Transports preserving the angle between two contravariant vector fields but changing their lengths proportional to their own lengths are introduced as "conformal" transports and investigated over [Formula: see text]-spaces. They are more general than the Fermi–Walker transports. In an analogous way as in the case of Fermi–Walker transports a conformal covariant differential operator and its conformal derivative are defined and considered over [Formula: see text]-spaces. Different special types of conformal transports are determined inducing also Fermi–Walker transports for orthogonal vector fields as special cases. Conditions under which the length of a non-null contravariant vector field could swing as a homogeneous harmonic oscillator are established. The results obtained regardless of any concrete field (gravitational) theory could have direct applications in such types of theories.

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10

Li, Yanlin, Santu Dey, Sampa Pahan, and Akram Ali. "Geometry of conformal η-Ricci solitons and conformal η-Ricci almost solitons on paracontact geometry." Open Mathematics 20, no. 1 (January 1, 2022): 574–89. http://dx.doi.org/10.1515/math-2022-0048.

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Abstract We prove that if an η \eta -Einstein para-Kenmotsu manifold admits a conformal η \eta -Ricci soliton then it is Einstein. Next, we proved that a para-Kenmotsu metric as a conformal η \eta -Ricci soliton is Einstein if its potential vector field V V is infinitesimal paracontact transformation or collinear with the Reeb vector field. Furthermore, we prove that if a para-Kenmotsu manifold admits a gradient conformal η \eta -Ricci almost soliton and the Reeb vector field leaves the scalar curvature invariant then it is Einstein. We also construct an example of para-Kenmotsu manifold that admits conformal η \eta -Ricci soliton and satisfy our results. We also have studied conformal η \eta -Ricci soliton in three-dimensional para-cosymplectic manifolds.

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11

Mihai, I., A. Oiagă, and R. Rosca. "On a class of even-dimensional manifolds structured by an affine connection." International Journal of Mathematics and Mathematical Sciences 29, no. 11 (2002): 681–86. http://dx.doi.org/10.1155/s0161171202011390.

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We deal with a2m-dimensional Riemannian manifold(M,g)structured by an affine connection and a vector field𝒯, defining a𝒯-parallel connection. It is proved that𝒯is both a torse forming vector field and an exterior concurrent vector field. Properties of the curvature2-forms are established. It is shown thatMis endowed with a conformal symplectic structureΩand𝒯defines a relative conformal transformation ofΩ.

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12

Olmo, Gonzalo J., Emanuele Orazi, and Gianfranco Pradisi. "Conformal metric-affine gravities." Journal of Cosmology and Astroparticle Physics 2022, no. 10 (October 1, 2022): 057. http://dx.doi.org/10.1088/1475-7516/2022/10/057.

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Abstract We revisit the gauge symmetry related to integrable projective transformations in metric-affine formalism, identifying the gauge field of the Weyl (conformal) symmetry as a dynamical component of the affine connection. In particular, we show how to include the local scaling symmetry as a gauge symmetry of a large class of geometric gravity theories, introducing a compensator dilaton field that naturally gives rise to a Stückelberg sector where a spontaneous breaking mechanism of the conformal symmetry is at work to generate a mass scale for the gauge field. For Ricci-based gravities that include, among others, General Relativity, f(R) and f(R, R μν R μν) theories and the EiBI model, we prove that the on-shell gauge vector associated to the scaling symmetry can be identified with the torsion vector, thus recovering and generalizing conformal invariant theories in the Riemann-Cartan formalism, already present in the literature.

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13

Rajeshwari, M. R., and S. K. Narasimhamurthy. "Conformal Vector fields on a locally projectively flat kropina metric." Journal of the Tensor Society 15, no. 01 (June 30, 2009): 62–74. http://dx.doi.org/10.56424/jts.v15i01.10612.

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In this paper, we study and characterize conformal vector fields on a Finsler manifold with the Kropina metric of projectively isotropic flag curvature. Further, we prove that any conformal vector field on a non-Riemannian locally projectively flat Kropina metric of dimension n greator than or equal to 3 must be homothetic and completely determine conformal vector fields on a locally projectively flat Kropina metric.

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14

Mihai, Ion, Radu Rosca, and Valentin Ghişoiu. "On Riemannian manifolds endowed with a locally conformal cosymplectic structure." International Journal of Mathematics and Mathematical Sciences 2005, no. 21 (2005): 3471–78. http://dx.doi.org/10.1155/ijmms.2005.3471.

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We deal with a locally conformal cosymplectic manifoldM(φ,Ω,ξ,η,g)admitting a conformal contact quasi-torse-forming vector fieldT. The presymplectic2-formΩis a locally conformal cosymplectic2-form. It is shown thatTis a3-exterior concurrent vector field. Infinitesimal transformations of the Lie algebra of∧Mare investigated. The Gauss map of the hypersurfaceMξnormal toξis conformal andMξ×Mξis a Chen submanifold ofM×M.

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15

Wang, Y., B. Liu, K. Zhou, and Y. Tong. "Vector Field Map Representation for Near Conformal Surface Correspondence." Computer Graphics Forum 37, no. 6 (November 28, 2017): 72–83. http://dx.doi.org/10.1111/cgf.13312.

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16

Diógenes, R., E. Ribeiro, and J. Silva Filho. "Gradient Ricci solitons admitting a closed conformal Vector field." Journal of Mathematical Analysis and Applications 455, no. 2 (November 2017): 1975–83. http://dx.doi.org/10.1016/j.jmaa.2017.06.071.

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17

Khuzwayo, Ntokozo Sibonelo, and Fortuné Massamba. "Some Properties of Curvature Tensors and Foliations of Locally Conformal Almost Kähler Manifolds." International Journal of Mathematics and Mathematical Sciences 2021 (February 17, 2021): 1–7. http://dx.doi.org/10.1155/2021/6673918.

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We investigate a class of locally conformal almost Kähler structures and prove that, under some conditions, this class is a subclass of almost Kähler structures. We show that a locally conformal almost Kähler manifold admits a canonical foliation whose leaves are hypersurfaces with the mean curvature vector field proportional to the Lee vector field. The geodesibility of the leaves is also characterized, and their minimality coincides with the incompressibility of the Lee vector field along the leaves.

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18

Oliver, Jesús. "A vector field method for non-trapping, radiating spacetimes." Journal of Hyperbolic Differential Equations 13, no. 04 (December 2016): 735–90. http://dx.doi.org/10.1142/s021989161650020x.

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We study the global decay properties of solutions to the linear wave equation in 1+3 dimensions on time-dependent, weakly asymptotically flat spacetimes. Assuming non-trapping of null geodesics and a local energy decay estimate, we prove that sufficiently regular solutions to this equation have bounded conformal energy. As an application we also show a conformal energy estimate with vector fields applied to the solution as well as a global [Formula: see text] decay bound in terms of a weighted norm on initial data. For solutions to the wave equation in these dynamical backgrounds, our results reduce the problem of establishing the classical pointwise decay rate [Formula: see text] in the interior and [Formula: see text] along outgoing null cones to simply proving that local energy decay holds.

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19

Zhang, Pengfei, Yanlin Li, Soumendu Roy, Santu Dey, and Arindam Bhattacharyya. "Geometrical Structure in a Perfect Fluid Spacetime with Conformal Ricci–Yamabe Soliton." Symmetry 14, no. 3 (March 17, 2022): 594. http://dx.doi.org/10.3390/sym14030594.

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The present paper aims to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci–Yamabe metric and conformal η-Ricci–Yamabe metric. We delineate the conditions for conformal Ricci–Yamabe soliton to be expanding, steady or shrinking. We also discuss conformal Ricci–Yamabe soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid and radiation era. Furthermore, we design conformal η-Ricci–Yamabe soliton to find its characteristics in a perfect fluid spacetime and lastly acquired Laplace equation from conformal η-Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type. Overall, the main novelty of the paper is to study the geometrical phenomena and characteristics of our newly introduced conformal Ricci–Yamabe and conformal η-Ricci–Yamabe solitons to apply their existence in a perfect fluid spacetime.

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20

Catalano, D. A. "Closed conformal vector fields on pseudo-Riemannian manifolds." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–8. http://dx.doi.org/10.1155/ijmms/2006/36545.

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21

siddiqi, Mohd Danish, and Shah Alam Siddiqui. "Conformal Ricci soliton and geometrical structure in a perfect fluid spacetime." International Journal of Geometric Methods in Modern Physics 17, no. 06 (May 2020): 2050083. http://dx.doi.org/10.1142/s0219887820500838.

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In this paper, we studied the geometrical aspects of a perfect fluid spacetime in terms of conformal Ricci soliton and conformal [Formula: see text]-Ricci soliton with torse-forming vector field [Formula: see text]. Condition for the conformal Ricci soliton to be steady, expanding or shrinking are also given. In particular case, when the potential vector filed [Formula: see text] of the soliton is of gradient type, we derive, from the conformal [Formula: see text]-Ricci soliton equation, a Laplacian equation.

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22

Yoldas, Halil. "Some Results on Cosymplectic Manifolds Admitting Certain Vector Fields." Journal of Geometry and Symmetry in Physics 60 (2021): 83–94. http://dx.doi.org/10.7546/jgsp-60-2021-83-94.

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The purpose of present paper is to study cosymplectic manifolds admitting certain special vector fields such as holomorphically planar conformal (in short HPC) vector field. First, we prove that an HPC vector field on a cosymplectic manifold is also a Jacobi-type vector field. Then, we obtain the necessary conditions for such a vector field to be Killing. Finally, we give an important characterization for a torse-forming vector field on such a manifold given as to be recurrent.

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23

NAKAYAMA, YU. "GRAVITY DUAL FOR REGGEON FIELD THEORY AND NONLINEAR QUANTUM FINANCE." International Journal of Modern Physics A 24, no. 32 (December 30, 2009): 6197–222. http://dx.doi.org/10.1142/s0217751x09047594.

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We study scale invariant but not necessarily conformal invariant deformations of nonrelativistic conformal field theories from the dual gravity viewpoint. We present the corresponding metric that solves the Einstein equation coupled with a massive vector field. We find that, within the class of metric we study, when we assume the Galilean invariance, the scale invariant deformation always preserves the nonrelativistic conformal invariance. We discuss applications to scaling regime of Reggeon field theory and nonlinear quantum finance. These theories possess scale invariance but may or may not break the conformal invariance, depending on the underlying symmetry assumptions.

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24

Qureshi, Muhammad Amer, Ghulam Shabbir, K. S. Mahomed, and Taha Aziz. "Classification of proper teleparallel conformal symmetry of spherically symmetric static spacetimes using diagonal tetrads." Modern Physics Letters A 35, no. 28 (August 6, 2020): 2050232. http://dx.doi.org/10.1142/s0217732320502326.

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We study proper teleparallel conformal vector fields in spherically symmetric static spacetimes. The main objective of this paper is to present the classification for the above-mentioned spacetimes. The problem has been examined by two methods: direct integration technique and diagonal tetrads. We show that the spherically symmetric static spacetimes do not admit proper teleparallel conformal vector field, so are actually the teleparallel killing vector fields.

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25

De, Uday Chand, and Carlo Alberto Mantica. "CONFORMALLY RECURRENT SPACE-TIMES ADMITTING A PROPER CONFORMAL VECTOR FIELD." Communications of the Korean Mathematical Society 29, no. 2 (April 30, 2014): 319–29. http://dx.doi.org/10.4134/ckms.2014.29.2.319.

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26

Defever, Filip, and Radu Rosca. "Locally conformal manifolds endowed with a skew-symmetric vector field." Publicationes Mathematicae Debrecen 63, no. 4 (October 1, 2003): 523–36. http://dx.doi.org/10.5486/pmd.2003.2731.

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27

Siddiqi, Mohd, de Uday, and Sharief Deshmukh. "Estimation of almost Ricci-Yamabe solitons on static spacetimes." Filomat 36, no. 2 (2022): 397–407. http://dx.doi.org/10.2298/fil2202397s.

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This research work examines the standard static spacetime (SSST) in terms of almost Ricci-Yamabe soliton with conformal vector field. It is shown that almost Ricci-Yamabe soliton in standard static spacetime with function ? satisfies Poisson-Laplace equation. Next, we consider the function ? is harmonic and discuss the harmonic aspect of almost Ricci-Yamabe soliton on SSST. In addition, we investigate the nature of almost Ricci-Yamabe soliton on SSST with non-rotating Killing vector field. Also, we exhibit that non-steady non shrinking almost Ricci-Yamabe soliton i.e., ?? 0 on smooth, connected, and non-compact SSST with Killing vector field satisfies the Schr?dinger equation for a smooth function ?. Finally, we study almost Ricci-Yamabe soliton on static perfect fluid and vacuum static spacetime with conformal Killing vector field.

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28

Vaisman, Izu. "Locally conformal symplectic manifolds." International Journal of Mathematics and Mathematical Sciences 8, no. 3 (1985): 521–36. http://dx.doi.org/10.1155/s0161171285000564.

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A locally conformal symplectic (l. c. s.) manifold is a pair(M2n,Ω)whereM2n(n>1)is a connected differentiable manifold, andΩa nondegenerate2-form onMsuch thatM=⋃αUα(Uα- open subsets).Ω/Uα=eσαΩα,σα:Uα→ℝ,dΩα=0. Equivalently,dΩ=ω∧Ωfor some closed1-formω. L. c. s. manifolds can be seen as generalized phase spaces of Hamiltonian dynamical systems since the form of the Hamilton equations is, in fact, preserved by homothetic canonical transformations. The paper discusses first Hamiltonian vector fields, and infinitesimal automorphisms (i. a.) on l. c. s. manifolds. If(M,Ω)has an i. a.Xsuch thatω(X)≠0, we say thatMis of the first kind andΩassumes the particular formΩ=dθ−ω∧θ. Such anMis a2-contact manifold with the structure forms(ω,θ), and it has a vertical2-dimensional foliationV. IfVis regular, we can give a fibration theorem which shows thatMis aT2-principal bundle over a symplectic manifold. Particularly,Vis regular for some homogeneous l. c. s, manifolds, and this leads to a general construction of compact homogeneous l. c. s, manifolds. Various related geometric results, including reductivity theorems for Lie algebras of i. a. are also given. Most of the proofs are adaptations of corresponding proofs in symplectic and contact geometry. The paper ends with an Appendix which states an analogous fibration theorem in Riemannian geometry.

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Sharma, Ramesh, and Sharief Deshmukh. "Ricci almost solitons with associated projective vector field." Advances in Geometry 22, no. 1 (January 1, 2022): 1–8. http://dx.doi.org/10.1515/advgeom-2021-0034.

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Abstract A Ricci almost soliton whose associated vector field is projective is shown to have vanishing Cotton tensor, divergence-free Bach tensor and Ricci tensor as conformal Killing. For the compact case, a sharp inequality is obtained in terms of scalar curvature.We show that every complete gradient Ricci soliton is isometric to the Riemannian product of a Euclidean space and an Einstein space. A complete K-contact Ricci almost soliton whose associated vector field is projective is compact Einstein and Sasakian.

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MOON, TAEYOON, JOOHAN LEE, and PHILLIAL OH. "CONFORMAL INVARIANCE IN EINSTEIN–CARTAN–WEYL SPACE." Modern Physics Letters A 25, no. 37 (December 7, 2010): 3129–43. http://dx.doi.org/10.1142/s0217732310034201.

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We consider conformally invariant form of the actions in Einstein, Weyl, Einstein–Cartan and Einstein–Cartan–Weyl space in general dimensions (> 2) and investigate the relations among them. In Weyl space, the observational consistency condition for the vector field determining non-metricity of the connection can be obtained from the equation of motion. In Einstein–Cartan space a similar role is played by the vector part of the torsion tensor. We consider the case where the trace part of the torsion is the Kalb–Ramond type of field. In this case, we express conformally invariant action in terms of two scalar fields of conformal weight -1, which can be cast into some interesting form. We discuss some applications of the result.

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31

Sarkar, Sumanjit, Santu Dey, and Xiaomin Chen. "Certain results of conformal and *-conformal Ricci soliton on para-cosymplectic and para-Kenmotsu manifolds." Filomat 35, no. 15 (2021): 5001–15. http://dx.doi.org/10.2298/fil2115001s.

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The goal of the paper is to deliberate conformal Ricci soliton and *-conformal Ricci soliton within the framework of paracontact geometry. Here we prove that if an ?-Einstein para-Kenmotsu manifold admits conformal Ricci soliton and *-conformal Ricci soliton, then it is Einstein. Further we have shown that 3-dimensional para-cosymplectic manifold is Ricci flat if the manifold satisfies conformal Ricci soliton where the soliton vector field is conformal. We have also constructed some examples of para-Kenmotsu manifold that admits conformal and *-conformal Ricci soliton and verify our results.

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De, Uday, Sameh Shenawy, and Bülent Ünal. "Sequential warped products: Curvature and conformal vector fields." Filomat 33, no. 13 (2019): 4071–83. http://dx.doi.org/10.2298/fil1913071d.

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In this note, we introduce a new type of warped products called as sequential warped products to cover a wider variety of exact solutions to Einstein?s field equation. First, we study the geometry of sequential warped products and obtain covariant derivatives, curvature tensor, Ricci curvature and scalar curvature formulas. Then some important consequences of these formulas are also stated. We provide characterizations of geodesics and two different types of conformal vector fields, namely, Killing vector fields and concircular vector fields on sequential warped product manifolds. Finally, we consider the geometry of two classes of sequential warped product space-time models which are sequential generalized Robertson-Walker space-times and sequential standard static space-times.

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33

NAKAYAMA, YU. "VECTOR BETA FUNCTION." International Journal of Modern Physics A 28, no. 31 (December 19, 2013): 1350166. http://dx.doi.org/10.1142/s0217751x13501662.

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We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta functions, Higgs-like relation among anomalous dimensions and a gradient property. We further conjecture that nonrenormalization holds if and only if the vector operator is conserved. The local renormalization group analysis guarantees the first three within power counting renormalization. We verify all the conjectures in conformal perturbation theories and holography in the weakly coupled gravity regime.

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34

Ramzan, Muhammad, Murtaza Ali, and Fiaz Hussain. "Conformal and Disformal Structure of 3D Circularly Symmetric Static Metric in f(R) Theory of Gravity." January 2020 39, no. 1 (January 1, 2020): 111–16. http://dx.doi.org/10.22581/muet1982.2001.11.

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Conformal vector fields are treated as generalization of homothetic vector fields while disformal vector fields are defined through disformal transformations which are generalization of conformal transformations, therefore it is important to study conformal and disformal vector fields. In this paper, conformal and disformal structure of 3D (Three Dimensional) circularly symmetric static metric is discussed in the framework of f(R) theory of gravity. The purpose of this paper is twofold. Firstly, we have found some dust matter solutions of EFEs (Einstein Field Equations) by considering 3D circularly symmetric static metric in the f(R) theory of gravity. Secondly, we have found CKVFs (Conformal Killing Vector Fields) and DKVFs (Disformal Killing Vector Fields) of the obtained solutions by means of some algebraic and direct integration techniques. A metric version of f(R) theory of gravity is used to explore the solutions and dust matter as a source of energy momentum tensor. This study reveals that no proper DVFs exists. Here, DVFs for the solutions under consideration are either HVFs (Homothetic Vector Fields) or KVFs (Killing Vector Fields) in the f(R) theory of gravity. In this study, two cases have been discussed. In the first case, both CKVFs and DKVFs become HVFs with dimension three. In the second case, there exists two subcases. In the first subcase, DKVFs become HVFs with dimension seven. In the second subcase, CKVFs and DKVFs become KVFs having dimension four.

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35

Cariñena, J. F., J. Clemente-Gallardo, J. A. Jover-Galtier, and G. Marmo. "Tangent bundle geometry from dynamics: Application to the Kepler problem." International Journal of Geometric Methods in Modern Physics 14, no. 03 (February 14, 2017): 1750047. http://dx.doi.org/10.1142/s0219887817500475.

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In this paper, we consider a manifold with a dynamical vector field and enquire about the possible tangent bundle structures which would turn the starting vector field into a second-order one. The analysis is restricted to manifolds which are diffeomorphic with affine spaces. In particular, we consider the problem in connection with conformal vector fields of second-order and apply the procedure to vector fields conformally related with the harmonic oscillator ([Formula: see text]-oscillators). We select one which covers the vector field describing the Kepler problem.

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36

Ashoka, S. R., C. S. Bagewadi, and Gurupadavva Ingalahalli. "Certain Results on Ricci Solitons in -Sasakian Manifolds." Geometry 2013 (July 15, 2013): 1–4. http://dx.doi.org/10.1155/2013/573925.

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We study Ricci solitons in -Sasakian manifolds and show that it is a shrinking or expanding soliton and the manifold is Einstein with Killing vector field. Further, we prove that if is conformal Killilng vector field, then the Ricci soliton in 3-dimensional -Sasakian manifolds is shrinking or expanding but cannot be steady.

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37

Raziani, R., and M. V. Takook. "Polarization tensor in de Sitter gauge gravity." International Journal of Modern Physics D 30, no. 05 (February 25, 2021): 2150035. http://dx.doi.org/10.1142/s0218271821500358.

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The gauge theory of the de Sitter group, [Formula: see text], in the ambient space formalism has been considered in this paper. This method is important to construction of the de Sitter super-conformal gravity and Quantum gravity. [Formula: see text] gauge vector fields are needed which correspond to [Formula: see text] generators of the de Sitter group. Using the gauge-invariant Lagrangian, the field equations of these vector fields have been obtained. The gauge vector field solutions are recalled. By using these solutions, the spin-[Formula: see text] gauge potentials has been constructed. There are two possibilities for presenting this tensor field: rank-[Formula: see text] symmetric and mixed symmetry rank-[Formula: see text] tensor fields. To preserve the conformal transformation, a spin-[Formula: see text] field must be represented by a mixed symmetry rank-[Formula: see text] tensor field, [Formula: see text]. This tensor field has been rewritten in terms of a generalized polarization tensor field and a de Sitter plane wave. This generalized polarization tensor field has been calculated as a combination of vector polarization, [Formula: see text], and tensor polarization of rank-2, [Formula: see text], which can be used in the gravitational wave consideration. There is a certain extent of arbitrariness in the choice of this tensor and we fix it in such a way that, in the limit, [Formula: see text], one obtains the polarization tensor in Minkowski spacetime. It has been shown that under some simple conditions, the spin-[Formula: see text] mixed symmetry rank-[Formula: see text] tensor field can be simultaneously transformed by unitary irreducible representation of de Sitter and conformal groups ([Formula: see text]).

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38

Rustanov, Aligadzhi R., and Elena A. Polkina. "SOME QUESTIONS OF GEOMETRY OF LOCALLY CONFORMAL KAHLER MANIFOLDS." UNIVERSITY NEWS. NORTH-CAUCASIAN REGION. NATURAL SCIENCES SERIES, no. 3 (215) (September 30, 2022): 23–28. http://dx.doi.org/10.18522/1026-2237-2022-3-23-28.

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Torso-forming vector fields, as well as their special cases (concircular, special concircular and recurrent) are used in many areas of differential geometry, for example, in conformal, geodesic, almost geodesic, holomorphically projective and other mappings and transformations. The presence of torso-forming vector fields on the space under consideration makes the geometry of this space more meaningful. It is of interest to study the geometry of spaces that admit recurrent vector fields. In this paper, the authors consider locally conformally Kahler manifolds with a recurrent Lie vector. Such manifolds are called recurrent locally conformally Kahler manifolds. The Lie form and the Lie vector are calculated explicitly. It is proved that the Lie vector of a locally conformally Kahler manifold of constant curvature is a concircular field. A recurrence criterion for a conformally flat locally conformally Kahler manifold is obtained. Some properties of conformally flat locally conformally Kahler manifolds are proved. It is proved that a compact manifold of constant curvature does not admit its own recurrent locally conformal Kahler structure.

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39

Wei, Zhang, and Yang Junfeng. "A Design of Vertical Polarized Conformal Antenna and Its Array Based on UAV Structure." International Journal of Antennas and Propagation 2017 (2017): 1–12. http://dx.doi.org/10.1155/2017/9769815.

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The designs of conformal antenna and its array usually need to combine with different carrier structures. As for cone or cylindrical carrier, through using of invasive weed optimization (IWO), the conformal array should be the optimized design as the antenna installation space requirements of cylindrical carrier; through adopting the antenna unit miniaturization method, it designs out a conformal antenna and makes it easier to be installed and the omnidirectional circular polarized beam is also realized. As for unmanned aircraft carrier, it designs out the low profile of conformal vertical polarization antenna unit; through using the electric field integral equation (EFIE) and electric/magnetic current combined-field integral equation (JMCFIE) and multilevel fast multipole algorithm (MLFMA), it analyzes the two different characteristics of unmanned aircraft carrier on the influence of antenna performance. The results obtained through experiments and JMCFIE analysis are in good agreement; according to unmanned aircraft carrier, it also designed out the antenna in X/K-band spectrum; through IWO, the antenna array is optimized; the test results show that the array scanning angle can reach the corresponding beam direction.

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40

Wang, Wenjie. "Notes on affine Killing and two-Killing vector fields." Mathematica Slovaca 72, no. 2 (March 28, 2022): 483–90. http://dx.doi.org/10.1515/ms-2022-0034.

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Abstract In this paper, we investigate the geometry of affine Killing and two-Killing vector fields on Riemannian manifolds. More specifically, a new characterization of an Euclidean space via the affine Killing vector fields are given. Some conditions for an affine Killing and two-Killing vector field to be a conformal (homothetic) or Killing one are provided.

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41

TAKANO, KAZUHIKO, and JAE-BOK JUN. "ON A CONFORMAL KILLING VECTOR FIELD IN A COMPACT ALMOST KAHLERIAN MANIFOLD." Bulletin of the Korean Mathematical Society 42, no. 1 (February 1, 2005): 1–4. http://dx.doi.org/10.4134/bkms.2005.42.1.001.

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42

Romero, Alfonso, and Miguel S{ánchez. "Completeness of compact Lorentz manifolds admitting a timelike conformal Killing vector field." Proceedings of the American Mathematical Society 123, no. 9 (September 1, 1995): 2831. http://dx.doi.org/10.1090/s0002-9939-1995-1257122-3.

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43

STANEV, YASSEN S., and IVAN T. TODOROV. "TOWARDS A CONFORMAL QED4 WITH A NONVANISHING CURRENT 2-POINT FUNCTION." International Journal of Modern Physics A 03, no. 04 (April 1988): 1023–49. http://dx.doi.org/10.1142/s0217751x88000448.

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The possibility of constructing a conformally invariant model of spinor quantum electrodynamics (QED) in four dimensions involving an anomalous dimension of the electron field and a general indecomposable conformal law for the Maxwell field Fµν is studied within the local indefinite metric framework making systematic use of conformal operator product expansions (OPEs). It is demonstrated that the standard elementary conformal law for Fµν, which is known to yield a vanishing current-current 2-point function leads to a trivial theory. On the other hand, the conformal invariant 2-point function <Jμ(x1)Jν(x2)> (proportional to the second order perturbation theory expression in a massless QED) gives rise to a soluble conformal model involving [Formula: see text] and a vector field Vµ with longitudinal correlation function. The question whether the model can be extended to include Fµν (rather than its divergence) remains unresolved.

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44

Voicu, Nicoleta. "Conformal maps between pseudo-Finsler spaces." International Journal of Geometric Methods in Modern Physics 15, no. 01 (December 19, 2017): 1850003. http://dx.doi.org/10.1142/s0219887818500032.

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The paper aims to initiate a systematic study of conformal mappings between Finsler spacetimes and, more generally, between pseudo-Finsler spaces. This is done by extending several results in pseudo-Riemannian geometry which are necessary for field-theoretical applications and by proposing a technique that reduces some problems involving pseudo-Finslerian conformal vector fields to their pseudo-Riemannian counterparts. Also, we point out, by constructing classes of examples, that conformal groups of flat (locally Minkowskian) pseudo-Finsler spaces can be much richer than both flat Finslerian and pseudo-Euclidean conformal groups.

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45

Apostolopoulos, Pantelis S. "Intrinsic conformal symmetries in Szekeres models." Modern Physics Letters A 32, no. 19 (May 25, 2017): 1750099. http://dx.doi.org/10.1142/s0217732317500997.

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We show that Spatially Inhomogeneous (SI) and Irrotational dust models admit a six-dimensional algebra of Intrinsic Conformal Vector Fields (ICVFs) [Formula: see text] satisfying [Formula: see text], where [Formula: see text] is the associated metric of the two-dimensional distribution [Formula: see text] normal to the fluid velocity [Formula: see text] and the radial unit space-like vector field [Formula: see text]. The Intrinsic Conformal (IC) algebra is determined for each of the curvature value [Formula: see text] that characterizes the structure of the screen space [Formula: see text]. In addition the conformal flatness of the hypersurfaces [Formula: see text] indicates the existence of a ten-dimensional algebra of ICVFs of the three-dimensional metric [Formula: see text]. We illustrate this expectation and propose a method to derive them by giving explicitly the seven proper ICVFs of the Lemaître–Tolman–Bondi (LTB) model which represents the simplest subclass within the Szekeres family.

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46

Gionti, Gabriele, and Andronikos Paliathanasis. "Duality transformation and conformal equivalent scalar–tensor theories." Modern Physics Letters A 33, no. 16 (May 30, 2018): 1850093. http://dx.doi.org/10.1142/s0217732318500931.

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We deal with the duality symmetry of the dilaton field in cosmology and specifically with the so-called Gasperini–Veneziano duality transformation. In particular, we determine two conformal equivalent theories to the dilaton field, and we show that under conformal transformations Gasperini–Veneziano duality symmetry does not survive. Moreover, we show that those theories share a common conservation law, of Noetherian kind, while the symmetry vector which generates the conservation law is an isometry only for the dilaton field. Finally, we show that the Lagrangian of the dilaton field is equivalent with the two-dimensional “hyperbolic oscillator” in a Lorentzian space whose O(d, d) invariance is transformed into the Gasperini–Veneziano duality invariance in the original coordinates.

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47

DAPPIAGGI, CLAUDIO, and DANIEL SIEMSSEN. "HADAMARD STATES FOR THE VECTOR POTENTIAL ON ASYMPTOTICALLY FLAT SPACETIMES." Reviews in Mathematical Physics 25, no. 01 (February 2013): 1350002. http://dx.doi.org/10.1142/s0129055x13500025.

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We develop a quantization scheme for the vector potential on globally hyperbolic spacetimes which realizes it as a locally covariant conformal quantum field theory. This result allows us to employ on a large class of backgrounds, which are asymptotically flat at null infinity, a bulk-to-boundary correspondence procedure in order to identify for the underlying field algebra a distinguished ground state which is of Hadamard form.

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48

Li, Tongzhu, and Demeter Krupka. "The Geometry of Tangent Bundles: Canonical Vector Fields." Geometry 2013 (April 14, 2013): 1–10. http://dx.doi.org/10.1155/2013/364301.

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A canonical vector field on the tangent bundle is a vector field defined by an invariant coordinate construction. In this paper, a complete classification of canonical vector fields on tangent bundles, depending on vector fields defined on their bases, is obtained. It is shown that every canonical vector field is a linear combination with constant coefficients of three vector fields: the variational vector field (canonical lift), the Liouville vector field, and the vertical lift of a vector field on the base of the tangent bundle.

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49

Chen, Zhizhi, Yanlin Li, Sumanjit Sarkar, Santu Dey, and Arindam Bhattacharyya. "Ricci Soliton and Certain Related Metrics on a Three-Dimensional Trans-Sasakian Manifold." Universe 8, no. 11 (November 11, 2022): 595. http://dx.doi.org/10.3390/universe8110595.

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In this article, a Ricci soliton and *-conformal Ricci soliton are examined in the framework of trans-Sasakian three-manifold. In the beginning of the paper, it is shown that a three-dimensional trans-Sasakian manifold of type (α,β) admits a Ricci soliton where the covariant derivative of potential vector field V in the direction of unit vector field ξ is orthogonal to ξ. It is also demonstrated that if the structure functions meet α2=β2, then the covariant derivative of V in the direction of ξ is a constant multiple of ξ. Furthermore, the nature of scalar curvature is evolved when the manifold of type (α,β) satisfies *-conformal Ricci soliton, provided α≠0. Finally, an example is presented to verify the findings.

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50

Zhang, Pengfei, Yanlin Li, Soumendu Roy, and Santu Dey. "Geometry of α-Cosymplectic Metric as ∗-Conformal η-Ricci–Yamabe Solitons Admitting Quarter-Symmetric Metric Connection." Symmetry 13, no. 11 (November 16, 2021): 2189. http://dx.doi.org/10.3390/sym13112189.

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The outline of this research article is to initiate the development of a ∗-conformal η-Ricci–Yamabe soliton in α-Cosymplectic manifolds according to the quarter-symmetric metric connection. Here, we have established some curvature properties of α-Cosymplectic manifolds in regard to the quarter-symmetric metric connection. Further, the attributes of the soliton when the manifold gratifies a quarter-symmetric metric connection have been displayed in this article. Later, we picked up the Laplace equation from ∗-conformal η-Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type, admitting quarter-symmetric metric connection. Next, we evolved the nature of the soliton when the vector field’s conformal killing reveals a quarter-symmetric metric connection. We show an example of a 5-dimensional α-cosymplectic metric as a ∗-conformal η-Ricci–Yamabe soliton acknowledges quarter-symmetric metric connection to prove our results.

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