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Journal articles on the topic 'Lorentzian'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Prakasha, D. G., and Vasant Chavan. "On M-Projective Curvature Tensor of Lorentzian α-Sasakian Manifolds." International Journal of Pure Mathematical Sciences 18 (August 2017): 22–31. http://dx.doi.org/10.18052/www.scipress.com/ijpms.18.22.

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In this paper, we study the nature of Lorentzianα-Sasakian manifolds admitting M-projective curvature tensor. We show that M-projectively flat and irrotational M-projective curvature tensor of Lorentzian α-Sasakian manifolds are locally isometric to unit sphere Sn(c) , wherec = α2. Next we study Lorentzianα-Sasakian manifold with conservative M-projective curvature tensor. Finally, we find certain geometrical results if the Lorentzianα-Sasakian manifold satisfying the relation M(X,Y)⋅R=0.

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2

Brändén and Huh. "Lorentzian polynomials." Annals of Mathematics 192, no. 3 (2020): 821. http://dx.doi.org/10.4007/annals.2020.192.3.4.

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3

Al-shehri, Norah, and Mohammed Guediri. "Semi-symmetric Lorentzian hypersurfaces in Lorentzian space forms." Journal of Geometry and Physics 71 (September 2013): 85–102. http://dx.doi.org/10.1016/j.geomphys.2013.04.007.

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4

Liu, Haiming, and Xiawei Chen. "Lorentzian Approximations and Gauss–Bonnet Theorem for E 1,1 with the Second Lorentzian Metric." Journal of Mathematics 2022 (October 28, 2022): 1–12. http://dx.doi.org/10.1155/2022/5402011.

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In this paper, we consider the Lorentzian approximations of rigid motions of the Minkowski plane E L 2 1,1 . By using the method of Lorentzian approximations, we define the notions of the intrinsic curvature for regular curves, the intrinsic geodesic curvature of regular curves on Lorentzian surface, and the intrinsic Gaussian curvature of Lorentzian surface in E 1,1 with the second Lorentzian metric away from characteristic points. Furthermore, we derive the expressions of those curvatures and prove Gauss–Bonnet theorem for the Lorentzian surface in E 1,1 with the second left-invariant Lorentzian metric g 2 .

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5

Lee, Ji-Eun. "Slant Curves and Contact Magnetic Curves in Sasakian Lorentzian 3-Manifolds." Symmetry 11, no. 6 (June 12, 2019): 784. http://dx.doi.org/10.3390/sym11060784.

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In this article, we define Lorentzian cross product in a three-dimensional almost contact Lorentzian manifold. Using a Lorentzian cross product, we prove that the ratio of κ and τ − 1 is constant along a Frenet slant curve in a Sasakian Lorentzian three-manifold. Moreover, we prove that γ is a slant curve if and only if M is Sasakian for a contact magnetic curve γ in contact Lorentzian three-manifold M. As an example, we find contact magnetic curves in Lorentzian Heisenberg three-space.

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6

Liu, Haiming, Xiawei Chen, Jianyun Guan, and Peifu Zu. "Lorentzian approximations for a Lorentzian $ \alpha $-Sasakian manifold and Gauss-Bonnet theorems." AIMS Mathematics 8, no. 1 (2022): 501–28. http://dx.doi.org/10.3934/math.2023024.

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<abstract><p>In this paper, we define the Lorentzian approximations of a $ 3 $-dimensional Lorentzian $ \alpha $-Sasakian manifold. Moreover, we define the notions of the intrinsic curvature for regular curves, the intrinsic geodesic curvature of regular curves on Lorentzian surfaces and spacelike surfaces and the intrinsic Gaussian curvature of Lorentzian surfaces and spacelike surfaces away from characteristic points. Furthermore, we derive the expressions of those curvatures and prove Gauss-Bonnet theorems for the Lorentzian surfaces and spacelike surfaces in the Lorentzian $ \alpha $-Sasakian manifold.</p></abstract>

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7

Bombelli, Luca. "Statistical Lorentzian geometry and the closeness of Lorentzian manifolds." Journal of Mathematical Physics 41, no. 10 (2000): 6944. http://dx.doi.org/10.1063/1.1288494.

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8

Gundogan, Halit. "Lorentzian matrix multiplication and the motions on Lorentzian plane." Glasnik Matematicki 41, no. 2 (December 15, 2006): 329–34. http://dx.doi.org/10.3336/gm.41.2.15.

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9

Chen, Bang-Yen. "Minimal flat Lorentzian surfaces in Lorentzian complex space forms." Publicationes Mathematicae Debrecen 73, no. 1-2 (July 1, 2008): 233–48. http://dx.doi.org/10.5486/pmd.2008.4247.

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10

Levinshtein, Michael, Valentin Dergachev, Alexander Dmitriev, and Pavel Shmakov. "Randomness and Earth’s Climate Variability." Fluctuation and Noise Letters 15, no. 01 (March 2016): 1650006. http://dx.doi.org/10.1142/s0219477516500061.

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Paleo-Sciences including palaeoclimatology and palaeoecology have accumulated numerous records related to climatic changes. The researchers have usually tried to identify periodic and quasi-periodic processes in these paleoscientific records. In this paper, we show that this analysis is incomplete. As follows from our results, random processes, namely processes with a single-time-constant [Formula: see text] (noise with a Lorentzian noise spectrum), play a very important and, perhaps, a decisive role in numerous natural phenomena. For several of very important natural phenomena the characteristic time constants [Formula: see text] are very similar and equal to [Formula: see text] years. However, this value of [Formula: see text] is not universal. For example, the spectral density fluctuations of the atmospheric radiocarbon [Formula: see text]C are characterized by a Lorentzian with [Formula: see text] years. The frequency dependence of spectral density fluctuations for benthic [Formula: see text]O records contains two Lorentzians with [Formula: see text] years and [Formula: see text] years.

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11

Perktas, Selcen Yüksel, Erol Kiliç, and Sadik Keles. "Hypersurfaces of Lorentzian para-Sasakian manifolds." MATHEMATICA SCANDINAVICA 109, no. 1 (September 1, 2011): 5. http://dx.doi.org/10.7146/math.scand.a-15174.

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In this paper we study the invariant and noninvariant hypersurfaces of $(1,1,1)$ almost contact manifolds, Lorentzian almost paracontact manifolds and Lorentzian para-Sasakian manifolds, respectively. We show that a noninvariant hypersurface of an $(1,1,1)$ almost contact manifold admits an almost product structure. We investigate hypersurfaces of affinely cosymplectic and normal $(1,1,1)$ almost contact manifolds. It is proved that a noninvariant hypersurface of a Lorentzian almost paracontact manifold is an almost product metric manifold. Some necessary and sufficient conditions have been given for a noninvariant hypersurface of a Lorentzian para-Sasakian manifold to be locally product manifold. We establish a Lorentzian para-Sasakian structure for an invariant hypersurface of a Lorentzian para-Sasakian manifold. Finally we give some examples for invariant and noninvariant hypersurfaces of a Lorentzian para-Sasakian manifold.

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12

Sari, Ramazan. "Some Properties Curvture of Lorentzian Kenmotsu Manifolds." Applied Mathematics and Nonlinear Sciences 5, no. 1 (March 31, 2020): 283–92. http://dx.doi.org/10.2478/amns.2020.1.00026.

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AbstractIn this paper different curvature tensors on Lorentzian Kenmotsu manifod are studied. We investigate constant ϕ–holomorphic sectional curvature and ℒ-sectional curvature of Lorentzian Kenmotsu manifolds, obtaining conditions for them to be constant of Lorentzian Kenmotsu manifolds in such condition. We calculate the Ricci tensor and scalar curvature for all the cases. Moreover we investigate some properties of semi invariant submanifolds of a Lorentzian Kenmotsu space form. We show that if a semi-invariant submanifold of a Lorentzian Kenmotsu space form M is totally geodesic, then M is an η−Einstein manifold. We consider sectional curvature of semi invariant product of a Lorentzian Kenmotsu manifolds.

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13

Franco, Nicolas. "Temporal Lorentzian spectral triples." Reviews in Mathematical Physics 26, no. 08 (September 2014): 1430007. http://dx.doi.org/10.1142/s0129055x14300076.

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We present the notion of temporal Lorentzian spectral triple which is an extension of the notion of pseudo-Riemannian spectral triple with a way to ensure that the signature of the metric is Lorentzian. A temporal Lorentzian spectral triple corresponds to a specific 3 + 1 decomposition of a possibly noncommutative Lorentzian space. This structure introduces a notion of global time in noncommutative geometry. As an example, we construct a temporal Lorentzian spectral triple over a Moyal–Minkowski spacetime. We show that, when time is commutative, the algebra can be extended to unbounded elements. Using such an extension, it is possible to define a Lorentzian distance formula between pure states with a well-defined noncommutative formulation.

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14

Wei, Sining, and Yong Wang. "Gauss—Bonnet Theorems in the Lorentzian Heisenberg Group and the Lorentzian Group of Rigid Motions of the Minkowski Plane." Symmetry 13, no. 2 (January 22, 2021): 173. http://dx.doi.org/10.3390/sym13020173.

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The aim of this paper was to obtain Gauss–Bonnet theorems on the Lorentzian Heisenberg group and the Lorentzian group of rigid motions of the Minkowski plane. At the same time, the sub-Lorentzian limits of Gaussian curvature for surfaces which are C2-smooth in the Lorentzian Heisenberg group away from characteristic points and signed geodesic curvature for curves which are C2-smooth on surfaces are studied. Using a similar method, we also studied the corresponding contents on Lorentzian group of rigid motions of the Minkowski plane.

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15

Andrejic, Vladica. "On Lorentzian spaces of constant sectional curvature." Publications de l'Institut Math?matique (Belgrade) 103, no. 117 (2018): 7–15. http://dx.doi.org/10.2298/pim1817007a.

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We investigate Osserman-like conditions for Lorentzian curvature tensors that imply constant sectional curvature. It is known that Osserman (moreover zwei-stein) Lorentzian manifolds have constant sectional curvature. We prove that some generalizations of the Rakic duality principle (Lorentzian totally Jacobi-dual or four-dimensional Lorentzian Jacobi-dual) imply constant sectional curvature. Moreover, any four-dimensional Jacobi-dual algebraic curvature tensor such that the Jacobi operator for some nonnull vector is diagonalizable, is Osserman. Additionally, any Lorentzian algebraic curvature tensor such that the reduced Jacobi operator for all nonnull vectors has a single eigenvalue has a constant sectional curvature.

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16

Perktaş, Selcen, Erol Kiliç, and Sadik Keleş. "Biharmonic Hypersurfaces of LP-Sasakian Manifolds." Annals of the Alexandru Ioan Cuza University - Mathematics 57, no. 2 (January 1, 2011): 387–408. http://dx.doi.org/10.2478/v10157-011-0034-z.

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Biharmonic Hypersurfaces of LP-Sasakian Manifolds In this paper the biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds are studied. We firstly find the biharmonic equation for a hypersurface which admits the characteristic vector field of the Lorentzian para-Sasakian as the normal vector field. We show that a biharmonic spacelike hypersurface of a Lorentzian para-Sasakian manifold with constant mean curvature is minimal. The biharmonicity condition for a hypersurface of a Lorentzian para-Sasakian manifold is investigated when the characteristic vector field belongs to the tangent hyperplane of the hypersurface. We find some necessary and sufficient conditions for a timelike hypersurface of a Lorentzian para-Sasakian manifold to be proper biharmonic. The nonexistence of proper biharmonic timelike hypersurfaces with constant mean curvature in a Ricci flat Lorentzian para-Sasakian manifold is proved.

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17

Kamishima, Yoshinobu. "Lorentzian similarity manifolds." Central European Journal of Mathematics 10, no. 5 (May 25, 2012): 1771–88. http://dx.doi.org/10.2478/s11533-012-0076-9.

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18

Figueroa-O'Farrill, José. "Non-lorentzian spacetimes." Differential Geometry and its Applications 82 (June 2022): 101894. http://dx.doi.org/10.1016/j.difgeo.2022.101894.

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19

Magid, Martin. "Lorentzian isoparametric hypersurfaces." Pacific Journal of Mathematics 118, no. 1 (May 1, 1985): 165–97. http://dx.doi.org/10.2140/pjm.1985.118.165.

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20

Cahen, Michel. "Lorentzian symmetric spaces." Bulletin de la Classe des sciences 9, no. 7 (1998): 325–30. http://dx.doi.org/10.3406/barb.1998.27940.

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21

Kar, Sayan, and Deshdeep Sahdev. "Evolving Lorentzian wormholes." Physical Review D 53, no. 2 (January 15, 1996): 722–30. http://dx.doi.org/10.1103/physrevd.53.722.

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22

Benisty, David, and Eduardo I. Guendelman. "Lorentzian quintessential inflation." International Journal of Modern Physics D 29, no. 14 (August 12, 2020): 2042002. http://dx.doi.org/10.1142/s021827182042002x.

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From the assumption that the slow-roll parameter [Formula: see text] has a Lorentzian form as a function of the e-folds number [Formula: see text], a successful model of a quintessential inflation is obtained. The form corresponds to the vacuum energy both in the inflationary and in the dark energy epochs. The form satisfies the condition to climb from small values of [Formula: see text] to [Formula: see text] at the end of the inflationary epoch. At the late universe, [Formula: see text] becomes small again and this leads to the dark energy epoch. The observables that the models predict fits with the latest Planck data: [Formula: see text]. Naturally, a large dimensionless factor that exponentially amplifies the inflationary scale and exponentially suppresses the dark energy scale appearance, producing a sort of cosmological seesaw mechanism. We find the corresponding scalar Quintessential Inflationary potential with two flat regions — one inflationary and one as a dark energy with slow-roll behavior.

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23

Giraud, B. G., Alan Lapedes, Lon Chang Liu, and J. C. Lemm. "Lorentzian neural nets." Neural Networks 8, no. 5 (January 1995): 757–67. http://dx.doi.org/10.1016/0893-6080(95)00019-v.

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24

Larsen, Jens Chr. "Lorentzian geodesic flows." Journal of Differential Geometry 43, no. 1 (1996): 119–70. http://dx.doi.org/10.4310/jdg/1214457900.

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25

Roman, Thomas A. "Inflating Lorentzian wormholes." Physical Review D 47, no. 4 (February 15, 1993): 1370–79. http://dx.doi.org/10.1103/physrevd.47.1370.

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26

Treumann, Rudolf A. "Generalized-Lorentzian Thermodynamics." Physica Scripta 59, no. 3 (March 1, 1999): 204–14. http://dx.doi.org/10.1238/physica.regular.059a00204.

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27

Alekseevski, Dmitri, and D. V. Alekseevski. "Selfsimilar Lorentzian manifolds." Annals of Global Analysis and Geometry 3, no. 1 (1985): 59–84. http://dx.doi.org/10.1007/bf00054491.

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28

Kunzinger, Michael, and Clemens Sämann. "Lorentzian length spaces." Annals of Global Analysis and Geometry 54, no. 3 (October 2018): 399–447. http://dx.doi.org/10.1007/s10455-018-9633-1.

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29

Calvaruso, Giovanni. "Contact Lorentzian manifolds." Differential Geometry and its Applications 29 (August 2011): S41—S51. http://dx.doi.org/10.1016/j.difgeo.2011.04.006.

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30

Gutiérrez, Manuel, and Olaf Müller. "Compact Lorentzian holonomy." Differential Geometry and its Applications 48 (October 2016): 11–22. http://dx.doi.org/10.1016/j.difgeo.2016.05.003.

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31

Park, Joon-Sang. "RIBAUCOUR TRANSFORMATIONS ON LORENTZIAN SPACE FORMS IN LORENTZIAN SPACE FORMS." Journal of the Korean Mathematical Society 45, no. 6 (November 1, 2008): 1577–90. http://dx.doi.org/10.4134/jkms.2008.45.6.1577.

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32

Pal Singh, Amrinder, Cyriaque Atindogbe, Rakesh Kumar, and Varun Jain. "Chen-like inequalities on null hypersurfaces with closed rigging of a Lorentzian manifold." International Journal of Geometric Methods in Modern Physics 18, no. 08 (June 4, 2021): 2150125. http://dx.doi.org/10.1142/s0219887821501255.

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We study null hypersurfaces of a Lorentzian manifold with a closed rigging for the hypersurface. We derive inequalities involving Ricci tensors, scalar curvature, squared mean curvatures for a null hypersurface with a closed rigging of a Lorentzian space form and for a screen homothetic null hypersurface of a Lorentzian manifold. We also establish a generalized Chen–Ricci inequality for a screen homothetic null hypersurface of a Lorentzian manifold with a closed rigging for the hypersurface.

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33

Rahman, Shamsur. "Characterization of Quarter Symmetric Non-Metric Connection on Transversal Hypersurfaces of Lorentzian para-Sasakian Manifolds." Journal of the Tensor Society 8, no. 01 (June 30, 2007): 65–75. http://dx.doi.org/10.56424/jts.v8i01.10557.

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In the present paper, quarter symmetric non metric connection on transversal hypersurfaces of Lorentzian para-Sasakian manifold is defined. It is studied the characterization of connections for product structure and it is shown that each transversal hypersurfaces of Lorentzian para-Sasakian manifold admits an almost product Lorentzian structure on a quarter symmetric non metric connection. Some characterization of transversal hypersurfaces of Lorentzian paraSasakian manifold with a quarter symmetric non metric connection are studied which are closed.

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34

Ahmad, Arjumand, and Shamsur Rahman. "A Note on Transversal hypersurfaces of Lorentzian para-Sasakian manifolds with a Semi-Symmetric Non-Metric Connection." Journal of the Tensor Society 8, no. 01 (June 30, 2007): 53–63. http://dx.doi.org/10.56424/jts.v8i01.10558.

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Transversal hypersurfaces of Lorentzian para-Sasakian manifold are defined. It is proved that the fundamental 2-form on the transversal hypersurfaces of Lorentzian para-Sasakian manifold with (f, g, u, v, λ)-structure are closed. In this paper it is shown that transversal hypersurfaces of Lorentzian para-Sasakian manifold admits a product structure with a semi symmetric non metric connection. It is shown that transversal hypersurfaces of Lorentzian para-Sasakian manifold with a semi symmetric non metric connection are closed

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35

Anitha, B. S., and C. S. Bagewadi. "Pseudoparallel Invariant Submanifolds of Lorentzian α-sasakian Manifolds." Journal of the Tensor Society 6, no. 01 (June 30, 2007): 11–25. http://dx.doi.org/10.56424/jts.v6i01.10465.

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In this paper, the study of an invariant submanifold of Lorentzian α- sasakian manifold is carried out and it is shown that, it is also Lorentzian α-sasakian. Further we prove that, if the second fundamental form of an invariant submanifold of Lorentzian α-sasakian manifold is recurrent, 2-recurrent and generalized 2-recurrent then the submanifold is totally geodesic and also an invariant submanifold of Lorentzian α-sasakian manifold with parallel third fundamental form is again totally geodesic. It is proved that pseudoparallel and 2-pseudoparallel invariant submanifolds of Lorentzian α-sasakian manifolds is also totally geodesic. Further, we also show that this property of totally geodesic holds true if e C · σ = L1Q(g, σ) and e C · e∇ σ = L1Q(g,e∇ σ).

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36

Prasad, Kripa Sindhu. "3-dimensional Locally φ−Concircularly symmetric Lorentzian β−Kenmotsu Manifold." Journal of the Tensor Society 12, no. 01 (June 30, 2007): 65–71. http://dx.doi.org/10.56424/jts.v12i01.10591.

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The present work deals with the study of 3-dimensional Locally ϕ− concircularly symmetric Lorentzian β−Kenmotsu manifold which generalizes the notion of locally concirculary-symmetric Lorentzian β−Kenmotsu manifold and obtain some interesting results. Also it is proved that a concircularly ϕ−recurrent Lorentzian β−Kenmotsu manifolds is an Einstein manifold and Proved that if a concircularly ϕ−recurrent Lorentzian β−Kenmotsu manifolds (m^{2n+1}, g), n > 1, has non zero constant sectional curvature, then it reduces to a concircularly locally ϕ−symmetric manifold.

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37

Faghfouri, Morteza, and Sahar Mashmouli. "On anti-invariant semi-Riemannian submersions from Lorentzian para-Sasakian manifolds." Filomat 32, no. 10 (2018): 3465–78. http://dx.doi.org/10.2298/fil1810465f.

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In this paper, we study a semi-Riemannian submersion from Lorentzian almost (para) contact manifolds and find necessary and sufficient conditions for the characteristic vector field to be vertical or horizontal. We also obtain decomposition theorems for anti-invariant semi-Riemannian submersions from Lorentzian para-Sasakian manifolds onto Lorentzian manifolds.

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38

Zhenqi, Li. "Lorentzian isoparametric hypersurfaces in the Lorentzian sphere $\boldsymbol{S_1^{n+1}}$." SCIENTIA SINICA Mathematica 48, no. 6 (April 23, 2018): 725. http://dx.doi.org/10.1360/n012017-00195.

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39

Park, Joonsang. "Lorentzian Submanifolds in Lorentzian Space Form with the Same Constant Curvatures." Geometriae Dedicata 108, no. 1 (October 2004): 93–104. http://dx.doi.org/10.1007/s10711-004-5458-0.

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40

Wahby, A. S. M., and J. Los. "Diffusion in Lorentzian and quasi-Lorentzian N2-light noble gas mixtures." Physica B+C 145, no. 1 (April 1987): 69–77. http://dx.doi.org/10.1016/0378-4363(87)90121-5.

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41

Wahby, A. S. M. "Diffusion in Lorentzian and quasi-Lorentzian N2-heavy noble gas mixtures." Physica B+C 145, no. 1 (April 1987): 78–83. http://dx.doi.org/10.1016/0378-4363(87)90122-7.

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42

CHEN, BANG-YEN, FRANKI DILLEN, and JOERI VAN DER VEKEN. "COMPLETE CLASSIFICATION OF PARALLEL LORENTZIAN SURFACES IN LORENTZIAN COMPLEX SPACE FORMS." International Journal of Mathematics 21, no. 05 (May 2010): 665–86. http://dx.doi.org/10.1142/s0129167x10006276.

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A surface of a pseudo-Riemannian manifold is called parallel if its second fundamental form is parallel with respect to the Van der Waerden–Bortolotti connection. Such surfaces are fundamental since the extrinsic invariants of the surfaces do no change from point to point. In this article, we completely classify parallel Lorentzian surfaces in Lorentzian complex space forms of complex dimension two.

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43

Gündoğan, Halit, and Siddika Özkaldi. "Clifford Product and Lorentzian Plane Displacements In 3-Dimensional Lorentzian Space." Advances in Applied Clifford Algebras 19, no. 1 (August 13, 2008): 43–50. http://dx.doi.org/10.1007/s00006-008-0124-5.

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44

CALVARUSO, G., and J. VAN DER VEKEN. "LORENTZIAN SYMMETRIC THREE-SPACES AND THE CLASSIFICATION OF THEIR PARALLEL SURFACES." International Journal of Mathematics 20, no. 10 (October 2009): 1185–205. http://dx.doi.org/10.1142/s0129167x09005728.

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We describe a global model for Lorentzian symmetric three-spaces admitting a parallel null vector field, and classify completely the surfaces with parallel second fundamental form in all Lorentzian symmetric three-spaces. Interesting differences arise with respect to the Riemannian case studied in [2]. Our results complete the classification of parallel surfaces in all three-dimensional Lorentzian homogeneous spaces.

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45

CALVARUSO, G., and B. DE LEO. "PSEUDO-SYMMETRIC LORENTZIAN THREE-MANIFOLDS." International Journal of Geometric Methods in Modern Physics 06, no. 07 (November 2009): 1135–50. http://dx.doi.org/10.1142/s0219887809004132.

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We investigate pseudo-symmetric Lorentzian three-manifolds for the different possible Segre types of the Ricci operator. After determining all three-dimensional pseudo-symmetric Lorentzian algebraic curvature tensors, we classify pseudo-symmetric Lorentzian three-spaces which are either homogeneous, curvature homogeneous up to order 1 or curvature homogeneous, and we also provide some examples which are not curvature homogeneous.

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46

Laha, Barnali, Bandana Das, and Arindam Bhattacharyya. "Contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold." Acta Universitatis Sapientiae, Mathematica 5, no. 2 (December 1, 2013): 157–68. http://dx.doi.org/10.2478/ausm-2014-0011.

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Abstract In this paper we prove some properties of the indefinite Lorentzian para-Sasakian manifolds. Section 1 is introductory. In Section 2 we define D-totally geodesic and D⊥-totally geodesic contact CRsubmanifolds of an indefinite Lorentzian para-Sasakian manifold and deduce some results concerning such a manifold. In Section 3 we state and prove some results on mixed totally geodesic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold. Finally, in Section 4 we obtain a result on the anti-invariant distribution of totally umbilic contact CR-submanifolds of an indefinite Lorentzian para-Sasakian manifold.

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47

Samui, Srimayee, and Uday Chand De. "On some classes of invariant submanifolds of lorentzian para-sasakian manifolds." Tamkang Journal of Mathematics 47, no. 2 (June 30, 2016): 207–20. http://dx.doi.org/10.5556/j.tkjm.47.2016.1868.

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The object of the present paper is to study invariant submanifolds of Lorenzian Para-Sasakian manifolds. We consider the recurrent and bi-recurrent invariant submanifolds of Lorentzian para-Sasakian manifolds and pseudo-parallel and generalized Ricci pseudo-parallel invariant submanifolds of Lorentzian para-Sasakian manifolds. Also we search for the conditions $\mathcal{Z}(X,Y)\cdot\alpha=fQ(g,\alpha)$ and $\mathcal{Z}(X,Y)\cdot\alpha=fQ(S,\alpha)$ on invariant submanifolds of Lorentzian para-Sasakian manifolds, where $\mathcal{Z}$ is the concircular curvature tensor. Finally, we construct an example of an invariant submanifold of Lorentzian para Sasakian manifold.

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48

Nagel, W., and W. Van Driessche. "Effect of forskolin on conductive anion pathways of toad skin." American Journal of Physiology-Cell Physiology 263, no. 1 (July 1, 1992): C166—C171. http://dx.doi.org/10.1152/ajpcell.1992.263.1.c166.

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The effect of the diterpene, forskolin, on pathways for conductive Cl- transport was analyzed using isolated skins of Bufo viridis. Forskolin did not stimulate the voltage-activated Cl- movement from mucosa to serosa; the Lorentzian component in the power density spectrum, which was present at serosa positive clamp potentials under control conditions, decreased significantly. The observation that stimulation of cytosolic adenosine 3'-5'-cyclic monophosphate (cAMP) by forskolin has no effect on the voltage-activated Cl- transport argues against control of this pathway by cAMP. Our data further demonstrate that the forskolin-activated Cl- conductive pathway is also permeable for NO3-. This pathway was studied in absence of mucosal Cl-, which eliminates Cl- movement through the voltage-activated pathway. With SO4(2-) and Cl- on the mucosal and serosal sides, respectively, this forskolin-induced pathway displayed a linear current-voltage relationship. The associated Lorentzians increased at serosa negative clamp potentials. Transepithelial current and plateau value of the Lorentzian were related by a quadratic function, which suggests voltage-independence of number and open-close probability of these conductance sites. Morphological sites for voltage-activated and forskolin-induced conductive Cl- transport remain to be identified.

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Ma, Rongsheng, and Donghe Pei. "Some Curvature Properties on Lorentzian Generalized Sasakian-Space-Forms." Advances in Mathematical Physics 2019 (December 19, 2019): 1–7. http://dx.doi.org/10.1155/2019/5136758.

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In this paper, we investigate the Lorentzian generalized Sasakian-space-form. We give the necessary and sufficient conditions for the Lorentzian generalized Sasakian-space-form to be projectively flat, conformally flat, conharmonically flat, and Ricci semisymmetric and their relationship between each other. As the application of our theorems, we study the Ricci almost soliton on conformally flat Lorentzian generalized Sasakian-space-form.

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50

Bi, Wanying, and Zhigang Wang. "Wavefronts of traveling trajectories of geometric particles." International Journal of Geometric Methods in Modern Physics 16, no. 11 (November 2019): 1950175. http://dx.doi.org/10.1142/s0219887819501755.

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Confining the traveling trajectory of a tachyon to the two-dimensional Lorentzian space forms, we describe the trajectory as a spacelike front in these Lorentzian space forms. Introducing the differential geometry of singular curves in Lorentzian space forms, that is, the hyperbolic space and de Sitter space, and applying the Legendrian duality theorems, we establish the moving frame along the front, whereby the definitions of the evolutes of spacelike fronts in Lorentzian space forms are presented and the geometric properties of these evolutes are investigated in detail. It is shown that these evolutes can be interpreted as wavefronts under the viewpoint of Legendrian singularity theory.

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