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Journal articles on the topic 'Conformal change of metric'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

Tiwari, Bankteshwar, and Manoj Kumar. "On Randers change of a Finsler space with mth-root metric." International Journal of Geometric Methods in Modern Physics 11, no. 10 (November 2014): 1450087. http://dx.doi.org/10.1142/s021988781450087x.

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In this paper, we find a condition under which a Finsler space with Randers change of mth-root metric is projectively related to a mth-root metric and also we find a condition under which this Randers transformed mth-root Finsler metric is locally dually flat. Moreover, if transformed Finsler metric is conformal to the mth-root Finsler metric, then we prove that both of them reduce to Riemannian metrics.

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2

Maleki, Maryam, Nasrin Sadeghzadeh, and Tahereh Rajabi. "On conformally related spherically symmetric Finsler metrics." International Journal of Geometric Methods in Modern Physics 13, no. 10 (October 26, 2016): 1650118. http://dx.doi.org/10.1142/s0219887816501188.

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In this paper, we study the projective invariant quantities in Finsler geometry which remain invariant under the conformal change of metrics. In particular, we obtain the necessary and sufficient conditions of a given Douglas and Weyl and generalized Douglas–Weyl (GDW) metric to be invariant under the conformal transformations. Finally, we introduce some explicit examples of these metrics. Also, some of these [Formula: see text]-conformal transformations of Einstein metrics are considered.

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3

CAPOVILLA, RICCARDO, RUBÉN CORDERO, and JEMAL GUVEN. "CONFORMAL INVARIANTS OF THE EXTRINSIC GEOMETRY OF RELATIVISTIC MEMBRANES." Modern Physics Letters A 11, no. 35 (November 20, 1996): 2755–69. http://dx.doi.org/10.1142/s0217732396002757.

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We examine the change induced in the worldsheet geometry of a relativistic membrane under a conformal rescaling of the spacetime metric. As the induced transformation of the intrinsic geometry is obvious, the extrinsic geometry can be transformed nontrivially. By identifying the worldsheet scalars which transform multiplicatively, we can construct actions for extended objects which are conformally invariant.

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4

Moradpour, H., A. Dehghani, and M. T. Mohammadi Sabet. "Dynamic black holes in an FRW background: Lemaître transformations." Modern Physics Letters A 30, no. 39 (December 7, 2015): 1550207. http://dx.doi.org/10.1142/s0217732315502077.

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Since the conformal transformations of metric do not change its causal structure, we use these transformations to embed the Lemaître metrics into the FRW background. In our approach, conformal transformation is in agreement with the universe expansion regimes. Indeed, we use the Lemaître metrics because the horizon singularity is eliminated in these metrics. Moreover, some physical and mathematical properties of the introduced metrics have been addressed. We show that the resultant metrics include event horizons while their physical radii are increasing as a function of the universe expansion which may provide suitable metrics for investigating the effects of the universe expansion on the black holes.

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5

Tiwari, Bankteshwar, and Ghanashyam Kr Prajapati. "On generalized Kropina change of mth root Finsler metric." International Journal of Geometric Methods in Modern Physics 14, no. 05 (April 13, 2017): 1750081. http://dx.doi.org/10.1142/s0219887817500815.

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In the present paper, we consider generalized Kropina change of [Formula: see text]th root Finsler metric and prove that it is locally projectively flat if and only if it is locally Minkowskian. We also establish a necessary and sufficient condition under which the generalized Kropina change of [Formula: see text]th root metric is locally dually flat. Further it is proved that a generalized Kropina change of [Formula: see text]th root metric cannot be conformal to an [Formula: see text]th root Finsler metric.

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6

Tayebi, Akbar. "On generalized 4-th root metrics of isotropic scalar curvature." Mathematica Slovaca 68, no. 4 (August 28, 2018): 907–28. http://dx.doi.org/10.1515/ms-2017-0154.

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AbstractBy an interesting physical perspective and a suitable contraction of the Riemannian curvature tensor in Finsler geometry, Akbar-Zadeh introduced the notion of scalar curvature for the Finsler metrics. A Finsler metric is called of isotropic scalar curvature if the scalar curvature depends on the position only. In this paper, we study the class of generalized 4-th root metrics. These metrics generalize 4-th root metrics which are used in Biology as ecological metrics. We find the necessary and sufficient condition under which a generalized 4-th root metric is of isotropic scalar curvature. Then, we find the necessary and sufficient condition under which the conformal change of a generalized 4-th root metric is of isotropic scalar curvature. Finally, we characterize the Bryant metrics of isotropic scalar curvature.

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7

Tayebi, Akbar. "On 4-th root metrics of isotropic scalar curvature." Mathematica Slovaca 70, no. 1 (February 25, 2020): 161–72. http://dx.doi.org/10.1515/ms-2017-0341.

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AbstractIn this paper, we prove that every non-Riemannian 4-th root metric of isotropic scalar curvature has vanishing scalar curvature. Then, we show that every 4-th root metric of weakly isotropic flag curvature has vanishing scalar curvature. Finally, we find the necessary and sufficient condition under which the conformal change of a 4-th root metric is of isotropic scalar curvature.

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8

Narasimhamurthy. "On $\beta$-Conformal Change of Douglas Type with $(\alpha, \beta)$-Metric." Journal of Advanced Research in Pure Mathematics 5, no. 1 (January 1, 2013): 65–71. http://dx.doi.org/10.5373/jarpm.1220.121411.

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9

YOUSSEF, NABIL L., S. H. ABED, and S. G. ELGENDI. "GENERALIZED β-CONFORMAL CHANGE OF FINSLER METRICS." International Journal of Geometric Methods in Modern Physics 07, no. 04 (June 2010): 565–82. http://dx.doi.org/10.1142/s0219887810004440.

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In this paper, we introduce and investigate a general transformation or change of Finsler metrics, which is referred to as a generalized β-conformal change: [Formula: see text] This transformation combines both β-change and conformal change in a general setting. The change, under this transformation, of the fundamental Finsler connections, together with their associated geometric objects, are obtained. Some invariants and various special Finsler spaces are investigated under this change. The most important changes of Finsler metrics existing in the literature are deduced from the generalized β-conformal change as special cases.

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10

Shukla, H. S., Neelam Mishra, and Vivek Shukla. "ON HYPERSURFACE OF THE FINSLER SPACE OBTAINED BY CONFORMAL β− CHANGE." Jnanabha 50, no. 01 (2020): 49–56. http://dx.doi.org/10.58250/jnanabha.2020.50106.

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The conformal β− change of Finsler metric L(x, y) is given by L∗(x, y) = eσ(x) f (L(x, y), β(x, y)), where σ(x) is a function of x, β(x, y) = b i (x)yi is a one-form on the underlying manifold Mn , and f(L(x, y), β(x, y)) is a homogeneous function of degree one in L and β. Let Fn and F∗n be Finsler spaces with metric functions L and L∗ respectively. In this paper we study the hypersurface of F∗n and find condition under which this hypersurface becomes a hyperplane of first kind, a hyperplane of second kind and a hyperplane of third kind. In this endeavour we connect quantities of F∗n with those of Fn . When the hypersurface of F∗n is a hyperplane of first kind, we investigate the conditions under which it becomes a Landsberg space, a Berwald space, or a locally Minkowskian space.

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11

R, ThippeswamyK, and Narasimhamurthy S. K. "CONFORMAL CHANGE OF DOUGLAS SPECIAL FINSLER SPACE WITH SECOND APPROXIMATE MATSUMATO METRIC." International Journal of Advanced Research 5, no. 4 (April 30, 2017): 1290–95. http://dx.doi.org/10.21474/ijar01/3946.

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12

LUO, FENG. "COMBINATORIAL YAMABE FLOW ON SURFACES." Communications in Contemporary Mathematics 06, no. 05 (October 2004): 765–80. http://dx.doi.org/10.1142/s0219199704001501.

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In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial Yamabe flow on the space of all piecewise flat metrics associated to a triangulated surface. We show that the flow either develops removable singularities or converges exponentially fast to a constant combinatorial curvature metric. If the singularity develops, we show that the singularity is always removable by a surgery procedure on the triangulation. We conjecture that after finitely many such surgery changes on the triangulation, the flow converges to the constant combinatorial curvature metric as time approaches infinity.

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13

Yallappa Kumbar, Mallikarjun, Narasimhamurthy Senajji Kampalappa, Thippeswamy Komalobiah Rajanna, and Kavyashree Ambale Rajegowda. "Killing Vector Fields in Generalized Conformalβ-Change of Finsler Spaces." Journal of Mathematics 2015 (2015): 1–5. http://dx.doi.org/10.1155/2015/456291.

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We consider a Finsler space equipped with a Generalized Conformalβ-change of metric and study the Killing vector fields that correspond between the original Finsler space and the Finsler space equipped with Generalized Conformalβ-change of metric. We obtain necessary and sufficient condition for a vector field Killing in the original Finsler space to be Killing in the Finsler space equipped with Generalized Conformalβ-change of metric.

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14

YOUSSEF, NABIL L., S. H. ABED, and S. G. ELGENDI. "GENERALIZED β-CONFORMAL CHANGE AND SPECIAL FINSLER SPACES." International Journal of Geometric Methods in Modern Physics 09, no. 03 (May 2012): 1250016. http://dx.doi.org/10.1142/s0219887812500168.

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This work is a continuation of the paper [Generalized beta-conformal change of Finsler metrics, Int. J. Geom. Meth. Mod. Phys. 7(4) (2010) 565–582]. In the present paper, we investigate the change of Finsler metrics [Formula: see text] which we refer to as a generalized β-conformal change. Under this change, we study some special Finsler spaces, namely, quasi-C-reducible, semi-C-reducible, C-reducible, C2-like, S3-like and S4-like Finsler spaces. We obtain some characterizations of the energy β-change, the Randers change and the Kropina change. We also obtain the transformation of the T-tensor under this change and study some interesting special cases. We then impose a certain condition on the generalized β-conformal change, which we call the b-condition, and investigate the geometric consequences of such a condition. Finally, we give the conditions under which a generalized β-conformal change is projective and generalize some known results in the literature.

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15

Cortés, Vicente, and Liana David. "Twist, elementary deformation and K/K correspondence in generalized geometry." International Journal of Mathematics 31, no. 10 (September 2020): 2050078. http://dx.doi.org/10.1142/s0129167x20500780.

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We define the conformal change and elementary deformation in generalized complex geometry. We apply Swann’s twist construction to generalized (almost) complex and Hermitian structures obtained by these operations and establish conditions for the Courant integrability of the resulting twisted structures. We associate to any appropriate generalized Kähler manifold [Formula: see text] with a Hamiltonian Killing vector field a new generalized Kähler manifold, depending on the choice of a pair of non-vanishing functions and compatible twist data. We study this construction when [Formula: see text] is toric, with emphasis on the four-dimensional case, and we apply it to deformations of the standard flat Kähler metric on [Formula: see text], the Fubini–Study metric on [Formula: see text] and the admissible Kähler metrics on Hirzebruch surfaces. As a further application, we recover the K/K (Kähler/Kähler) correspondence, by specializing to ordinary Kähler manifolds.

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16

Alegre, Pablo, and Alfonso Carriazo. "Generalized Sasakian Space Forms and Conformal Changes of the Metric." Results in Mathematics 59, no. 3-4 (April 2, 2011): 485–93. http://dx.doi.org/10.1007/s00025-011-0115-z.

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17

Blair, D. E., and J. A. Oubiña. "Conformal and related changes of metric on the product of two almost contact metric manifolds." Publicacions Matemàtiques 34 (January 1, 1990): 199–207. http://dx.doi.org/10.5565/publmat_34190_15.

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18

Naito, Hisashi, and Hajime Urakawa. "Conformal change of Riemannian metrics and biharmonic maps." Indiana University Mathematics Journal 63, no. 6 (2014): 1631–57. http://dx.doi.org/10.1512/iumj.2014.63.5424.

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19

Cruz-Blázquez, Sergio, and David Ruiz. "Prescribing Gaussian and Geodesic Curvature on Disks." Advanced Nonlinear Studies 18, no. 3 (August 1, 2018): 453–68. http://dx.doi.org/10.1515/ans-2018-2021.

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Abstract In this paper, we consider the problem of prescribing the Gaussian and geodesic curvature on a disk and its boundary, respectively, via a conformal change of the metric. This leads us to a Liouville-type equation with a non-linear Neumann boundary condition. We address the question of existence by setting the problem in a variational framework which seems to be completely new in the literature. We are able to find minimizers under symmetry assumptions.

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20

Ferraris, Marco, Mauro Francaviglia, and Igor Volovich. "A Model of Affine Gravity in Two Dimensions and Plurality of Topology." International Journal of Modern Physics A 12, no. 28 (November 10, 1997): 5067–80. http://dx.doi.org/10.1142/s0217751x9700270x.

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A new model of two-dimensional gravity with an action depending only on a linear connection is suggested. This model is a topological one, in the sense that the classical action does not contain a metric or zweibein at all. A metric and an additional vector field are instead generated in the process of solving the equations of motion for the connection. The general solution of these equations of motion is given by an arbitrary Weyl connection which can be described by using the space of orbits under the action of the conformal group in the functional space containing all pairs formed by a metric and a vector field. By choosing a gauge one obtains a constant curvature equation. It is shown that this model admits an equivalent description by using a family of Lagrangians depending on the metric and the connection as independent variables. We show that nonlinear Lagrangians in the first order formalism lead to plurality of topology for the manifolds under consideration and give a simple general mechanism of governing topology change.

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21

Dzhunushaliev, Vladimir, and Vladimir Folomeev. "Spinor field solutions in F(B2) modified Weyl gravity." International Journal of Modern Physics D 29, no. 13 (September 3, 2020): 2050094. http://dx.doi.org/10.1142/s0218271820500947.

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We consider modified Weyl gravity where a Dirac spinor field is nonminimally coupled to gravity. It is assumed that such modified gravity is some approximation for the description of quantum gravitational effects related to the gravitating spinor field. It is shown that such a theory contains solutions for a class of metrics which are conformally equivalent to the Hopf metric on the Hopf fibration. For this case, we obtain a full discrete spectrum of the solutions and show that they can be related to the Hopf invariant on the Hopf fibration. The expression for the spin operator in the Hopf coordinates is obtained. It is demonstrated that this class of conformally equivalent metrics contains the following: (a) a metric describing a toroidal wormhole without exotic matter; (b) a cosmological solution with a bounce and inflation and (c) a transition with a change in metric signature. A physical discussion of the results is given.

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22

Rajabi, Tahere, Nasrin Sadeghzadeh, and Maryam Maleki. "On invariant Finsler metrics under (almost) β-changes." International Journal of Geometric Methods in Modern Physics 14, no. 11 (October 23, 2017): 1750156. http://dx.doi.org/10.1142/s0219887817501560.

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In this paper, we are going to study some [Formula: see text]-changes of the special class of Finsler metrics which we refer to as the (almost) [Formula: see text]-change and generalized (almost) [Formula: see text]-conformal changes. We investigate Douglas and Weyl tensors under these changes. In particular, we find the necessary and sufficient conditions for the Douglas metrics to be invariant under these type of changes.

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23

Di Cristo, Michele, and Luca Rondi. "The distance from the boundary in a Riemannian manifold: regularity up to a conformal change of the metric." Indiana University Mathematics Journal 70, no. 4 (2021): 1283–302. http://dx.doi.org/10.1512/iumj.2021.70.8620.

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24

SALAVESSA, ISABEL M. C., and ANA PEREIRA DO VALE. "TRANSGRESSION FORMS IN DIMENSION 4." International Journal of Geometric Methods in Modern Physics 03, no. 05n06 (September 2006): 1221–54. http://dx.doi.org/10.1142/s0219887806001442.

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We compute explicit transgression forms for the Euler and Pontrjagin classes of a Riemannian manifold M of dimension 4 under a conformal change of the metric, or a change to a Riemannian connection with torsion. These formulas describe the singular set of some connections with singularities on compact manifolds as a residue formula in terms of a polynomial of invariants. We give some applications for minimal submanifolds of Kähler manifolds. We also express the difference of the first Chern class of two almost complex structures, and in particular an obstruction to the existence of a homotopy between them, by a residue formula along the set of anti-complex points. Finally we take the first steps in the study of obstructions for two almost quaternionic-Hermitian structures on a manifold of dimension 8 to have homotopic fundamental forms or isomorphic twistor spaces.

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25

Zhang, Jun, and Ting-Kam Leonard Wong. "λ-Deformation: A Canonical Framework for Statistical Manifolds of Constant Curvature." Entropy 24, no. 2 (January 27, 2022): 193. http://dx.doi.org/10.3390/e24020193.

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This paper systematically presents the λ-deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry. We show that, based on deforming the Legendre duality, all objects in the Hessian case have their correspondence in the λ-deformed case: λ-convexity, λ-conjugation, λ-biorthogonality, λ-logarithmic divergence, λ-exponential and λ-mixture families, etc. In particular, λ-deformation unifies Tsallis and Rényi deformations by relating them to two manifestations of an identical λ-exponential family, under subtractive or divisive probability normalization, respectively. Unlike the different Hessian geometries of the exponential and mixture families, the λ-exponential family, in turn, coincides with the λ-mixture family after a change of random variables. The resulting statistical manifolds, while still carrying a dualistic structure, replace the Hessian metric and a pair of dually flat conjugate affine connections with a conformal Hessian metric and a pair of projectively flat connections carrying constant (nonzero) curvature. Thus, λ-deformation is a canonical framework in generalizing the well-known dually flat Hessian structure of information geometry.

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26

Baby, Sruthy Asha, and Gauree Shanker. "On Randers-conformal change of Finsler space with special (\alpha,\beta)-metrics." International Journal of Contemporary Mathematical Sciences 11 (2016): 415–23. http://dx.doi.org/10.12988/ijcms.2016.6846.

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27

Gwynne, Ewain, Jason Miller, and Scott Sheffield. "The Tutte Embedding of the Poisson–Voronoi Tessellation of the Brownian Disk Converges to $$\sqrt{8/3}$$-Liouville Quantum Gravity." Communications in Mathematical Physics 374, no. 2 (November 4, 2019): 735–84. http://dx.doi.org/10.1007/s00220-019-03610-5.

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Abstract Recent works have shown that an instance of a Brownian surface (such as the Brownian map or Brownian disk) a.s. has a canonical conformal structure under which it is equivalent to a $$\sqrt{8/3}$$8/3-Liouville quantum gravity (LQG) surface. In particular, Brownian motion on a Brownian surface is well-defined. The construction in these works is indirect, however, and leaves open a basic question: is Brownian motion on a Brownian surface the limit of simple random walk on increasingly fine discretizations of that surface, the way Brownian motion on $$\mathbb {R}^2$$R2 is the $$\epsilon \rightarrow 0$$ϵ→0 limit of simple random walk on $$\epsilon \mathbb {Z}^2$$ϵZ2? We answer this question affirmatively by showing that Brownian motion on a Brownian surface is (up to time change) the $$\lambda \rightarrow \infty $$λ→∞ limit of simple random walk on the Voronoi tessellation induced by a Poisson point process whose intensity is $$\lambda $$λ times the associated area measure. Among other things, this implies that as $$\lambda \rightarrow \infty $$λ→∞ the Tutte embedding (a.k.a. harmonic embedding) of the discretized Brownian disk converges to the canonical conformal embedding of the continuum Brownian disk, which in turn corresponds to $$\sqrt{8/3}$$8/3-LQG. Along the way, we obtain other independently interesting facts about conformal embeddings of Brownian surfaces, including information about the Euclidean shapes of embedded metric balls and Voronoi cells. For example, we derive moment estimates that imply, in a certain precise sense, that these shapes are unlikely to be very long and thin.

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28

Zheng, Tao. "The Chern–Ricci Flow on Oeljeklaus–Toma Manifolds." Canadian Journal of Mathematics 69, no. 1 (February 1, 2017): 220–40. http://dx.doi.org/10.4153/cjm-2015-053-0.

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AbstractWe study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus–Toma (OT-) manifolds that are non-Kähler compact complex manifolds with negative Kodaira dimension. We prove that after an initial conformal change, the flow converges in the Gromov–Hausdorff sense to a torus with a flat Riemannianmetric determined by the OT-manifolds themselves.

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29

March, Peter, Maung Min-Oo, and Ernst A. Ruh. "Mean Curvature of Riemannian Foliations." Canadian Mathematical Bulletin 39, no. 1 (March 1, 1996): 95–105. http://dx.doi.org/10.4153/cmb-1996-012-4.

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AbstractIt is shown that a suitable conformai change of the metric in the leaf direction of a transversally oriented Riemannian foliation on a closed manifold will make the basic component of the mean curvature harmonic. As a corollary, we deduce vanishing and finiteness theorems for Riemannian foliations without assuming the harmonicity of the basic mean curvature.

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30

Sedaghat, M. K., and B. Bidabad. "On a class of complete Finsler manifolds." International Journal of Mathematics 26, no. 11 (October 2015): 1550091. http://dx.doi.org/10.1142/s0129167x15500913.

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Here, it is shown that if a forward geodesically complete Finsler manifold admits a circle preserving change of metric then its indicatrix is conformally diffeomorphic to the Euclidean sphere Sn-1. Moreover, if the Finsler manifold is absolutely homogeneous and of scalar flag curvature then it is a Riemannian manifold of constant sectional curvature. These results provide a geometric interpretation for existence of solutions to the certain ODE on the Riemannian tangent space.

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31

Clayton, J. D. "Finsler-geometric continuum mechanics and the micromechanics of fracture in crystals." Journal of Micromechanics and Molecular Physics 01, no. 03n04 (October 2016): 1640003. http://dx.doi.org/10.1142/s2424913016400038.

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A continuum theory for the mechanical response of solid bodies subjected to potentially finite deformation is further developed and applied to solve several new problems in the context of the micromechanics of crystalline solids. The theory invokes concepts from Finsler differential geometry, and it provides a diffuse interface description of fracture surfaces. The director or internal state vector is associated with an order parameter describing degradation of the solid. Here, the deformation gradient between pseudo-Finsler reference and spatial configuration spaces is decomposed into a product of two terms, neither necessarily integrable to a vector field. The first is the recoverable elastic deformation, the second is the residual deformation attributed to changes in free volume in failure zones. The latter is restricted to spherical or isotropic symmetry; resulting Euler–Lagrange equations for mechanical and state variable equilibrium are derived. Metric tensors and volume elements depend on the internal state via a conformal transformation, i.e., Weyl scaling. This version of the theory is first applied to tensile fracture of magnesium. Analytical solutions demonstrate the model's capability to predict ductile versus brittle fracture depending on incorporation of Weyl scaling, with results aligned with molecular dynamics (MD) simulations. The second application is shear fracture in boron carbide: solutions depict weakening and tensile pressure in conjunction with structural collapse in shear transformation zones, as suggested by experiments, quantum mechanics, and/or MD simulations.

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32

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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33

Fabbri, Luca. "Metric-torsional conformal gravity." Physics Letters B 707, no. 5 (February 2012): 415–17. http://dx.doi.org/10.1016/j.physletb.2012.01.008.

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34

Herron, David A., William Ma, and David Minda. "Estimates for Conformal Metric Ratios." Computational Methods and Function Theory 5, no. 2 (February 2006): 323–45. http://dx.doi.org/10.1007/bf03321101.

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35

Ni, Yilong, and Meijun Zhu. "One-dimensional conformal metric flow." Advances in Mathematics 218, no. 4 (July 2008): 983–1011. http://dx.doi.org/10.1016/j.aim.2008.02.006.

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36

Xia, Hongchuan, and Chunping Zhong. "On complex Berwald metrics which are not conformal changes of complex Minkowski metrics." Advances in Geometry 18, no. 3 (July 26, 2018): 373–84. http://dx.doi.org/10.1515/advgeom-2017-0062.

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AbstractWe investigate a class of complex Finsler metrics on a domain D ⊂ ℂn. Necessary and sufficient conditions for these metrics to be strongly pseudoconvex complex Finsler metrics, or complex Berwald metrics, are given. The complex Berwald metrics constructed in this paper are neither trivial Hermitian metrics nor conformal changes of complex Minkowski metrics. We give a characterization of complex Berwald metrics which are of isotropic holomorphic curvatures, and also give characterizations of complex Finsler metrics of this class to be Kähler Finsler or weakly Kähler Finsler metrics. Moreover, in the strongly convex case, we give characterizations of complex Finsler metrics of this class to be projectively flat Finsler metrics or dually flat Finsler metrics.

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37

Arbuzov, Andrej B., and Alexander E. Pavlov. "Reduced conformal geometrodynamics." International Journal of Modern Physics A 35, no. 02n03 (January 30, 2020): 2040023. http://dx.doi.org/10.1142/s0217751x20400230.

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The global time in geometrodynamics is defined in a covariant under diffeomorphisms form. An arbitrary static background metric is taken in the tangent space. The global intrinsic time is identified with the mean value of the logarithm of the square root of the ratio of the metric determinants. The procedures of the Hamiltonian reduction and deparametrization of dynamical systems are implemented. The reduced Hamiltonian equations of motion of gravitational field in semi-geodesic coordinate system are written.

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38

DE BERREDO-PEIXOTO, GUILHERME, ANDRÉ PENNA-FIRME, and ILYA L. SHAPIRO. "ONE-LOOP DIVERGENCES OF QUANTUM GRAVITY USING CONFORMAL PARAMETRIZATION." Modern Physics Letters A 15, no. 38n39 (December 21, 2000): 2335–43. http://dx.doi.org/10.1142/s0217732300002929.

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We calculate the one-loop divergences for quantum gravity with cosmological constant, using new parametrization of quantum metric. The conformal factor of the metric is treated as an independent variable. As a result the theory possesses an additional degeneracy and one needs an extra conformal gauge fixing. We verify the on-shell independence of the divergences from the parameter of the conformal gauge fixing, and find a special conformal gauge in which the divergences coincide with the ones obtained by 't Hooft and Veltman (1974). Using conformal invariance of the counterterms, one can restore the divergences for the conformal metric–scalar gravity.

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39

ROD GOVER, A., and F. LEITNER. "A SUB-PRODUCT CONSTRUCTION OF POINCARÉ–EINSTEIN METRICS." International Journal of Mathematics 20, no. 10 (October 2009): 1263–87. http://dx.doi.org/10.1142/s0129167x09005753.

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Given any two Einstein (pseudo-)metrics, with scalar curvatures suitably related, we give an explicit construction of a Poincaré–Einstein (pseudo-)metric with conformal infinity the conformal class of the product of the initial metrics. We show that these metrics are equivalent to ambient metrics for the given conformal structure. The ambient metrics have holonomy that agrees with the conformal holonomy. In the generic case the ambient metric arises directly as a product of the metric cones over the original Einstein spaces. In general the conformal infinity of the Poincaré metric we construct is not Einstein, and so this describes a class of non-conformally Einstein metrics for which the (Fefferman–Graham) obstruction tensor vanishes.

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40

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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41

HAMADA, KEN-JI. "CONFORMAL FIELD THEORY ON R × S3 FROM QUANTIZED GRAVITY." International Journal of Modern Physics A 24, no. 16n17 (July 10, 2009): 3073–110. http://dx.doi.org/10.1142/s0217751x0904422x.

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Conformal algebra on R × S3 derived from quantized gravitational fields is examined. The model we study is a renormalizable quantum theory of gravity in four dimensions described by a combined system of the Weyl action for the traceless tensor mode and the induced Wess–Zumino action managing nonperturbative dynamics of the conformal factor in the metric field. It is shown that the residual diffeomorphism invariance in the radiation+ gauge is equal to the conformal symmetry, and the conformal transformation preserving the gauge-fixing condition that forms a closed algebra quantum mechanically is given by a combination of naive conformal transformation and a certain field-dependent gauge transformation. The unitarity issue of gravity is discussed in the context of conformal field theory. We construct physical states by solving the conformal invariance condition and calculate their scaling dimensions. It is shown that the conformal symmetry mixes the positive-metric and the negative-metric modes and thus the negative-metric mode does not appear independently as a gauge invariant state at all.

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42

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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Satou, Takafumi. "Conformal flatness of circle bundle metric." Tsukuba Journal of Mathematics 22, no. 2 (October 1998): 349–55. http://dx.doi.org/10.21099/tkbjm/1496163586.

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Mineyev, Igor. "Metric conformal structures and hyperbolic dimension." Conformal Geometry and Dynamics of the American Mathematical Society 11, no. 11 (November 1, 2007): 137–64. http://dx.doi.org/10.1090/s1088-4173-07-00165-8.

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Nicolas, Jean-Philippe. "Conformal scattering on the Schwarzschild metric." Annales de l'Institut Fourier 66, no. 3 (2016): 1175–216. http://dx.doi.org/10.5802/aif.3034.

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Bravetti, Alessandro, Cesar S. Lopez-Monsalvo, Francisco Nettel, and Hernando Quevedo. "The conformal metric structure of Geometrothermodynamics." Journal of Mathematical Physics 54, no. 3 (March 2013): 033513. http://dx.doi.org/10.1063/1.4795136.

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Herron, David A., and Pekka Koskela. "Conformal capacity and the quasihyperbolic metric." Indiana University Mathematics Journal 45, no. 2 (1996): 0. http://dx.doi.org/10.1512/iumj.1996.45.1966.

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Tsamparlis, Michael. "Conformal reduction of a spacetime metric." Classical and Quantum Gravity 15, no. 9 (September 1, 1998): 2901–8. http://dx.doi.org/10.1088/0264-9381/15/9/031.

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Di Prisco, A., L. Herrera, J. Jimenez, V. Galina, and J. Ibáñez. "The Bondi metric and conformal motions." Journal of Mathematical Physics 28, no. 11 (November 1987): 2692–96. http://dx.doi.org/10.1063/1.527713.

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Han, Bang-Xian. "Conformal Transformation on Metric Measure Spaces." Potential Analysis 51, no. 1 (May 16, 2018): 127–46. http://dx.doi.org/10.1007/s11118-018-9705-7.

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