On some basic curvature invariants of screen homothetic lightlike hypersurfaces in a GRW spacetime

被引：1

作者：

Harry, Idrees Fayaz ^{[1
]}

Lone, Mehraj Ahmad ^{[1
]}

Vilcu, Alina-Daniela ^{[2
]}

Vilcu, Gabriel-Eduard ^{[3
,4
,5
]}

机构：

[1] Natl Inst Technol, Dept Math, Srinagar 190006, Jammu & Kashmir, India

[2] Petr Gas Univ Ploiesti, Dept Informat Technol Math & Phys, Bd Bucuresti 39, Ploiesti 100680, Romania

[3] Univ Politehn Bucuresti, Dept Math & Informat, Splaiul Independentei 313, Bucharest 060042, Romania

[4] Romanian Acad, Gheorghe Mihoc Caius Iacob Inst Math Stat & Appl M, Calea 13 Septembrie 13, Bucharest 050711, Romania

[5] Univ Bucharest, Res Ctr Geometry Topol & Algebra, Str Acad 14, Bucharest 70109, Romania

来源：

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2024年 / 94卷

关键词：

Lightlike hypersurface; Generalized Robertson-Walker; spacetime; delta-Casorati curvature; Shape operator; LAGRANGIAN SUBMANIFOLDS; CLASSIFICATION;

D O I：

10.1016/j.difgeo.2024.102140

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This study is focused on the investigation of lightlike hypersurfaces of a generalized Robertson -Walker (GRW) spacetime. Recently, Poyraz (2022) [51,52] established some basic inequalities involving various curvature invariants of screen homothetic lightlike hypersurfaces of GRW spacetimes, like k -scalar curvature and k -Ricci curvature. In this work, we consider other basic curvature invariants, namely the scalar curvature and delta-Casorati curvatures, and derive new inequalities for such hypersurfaces of a GRW spacetime. We also find the conditions for which the equality cases in these inequalities hold and give some applications in Lorentzian geometry. (c) 2024 Elsevier B.V. All rights reserved.

引用

页数：18

共 54 条

[1] [Anonymous], 1996, Pure and Applied Mathematics
[2] Antidogbe C., 2004, Int. J. Pure Appl. Math., V11, P421
[3] Classification of Casorati ideal Lagrangian submanifolds in complex space forms
Aquib, Mohd.
Lee, Jae Won
Vilcu, Gabriel-Eduard
Yoon, Dae Won
[J]. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 2019, 63 : 30 - 49
[4] Atindogbe C., 2006, Kodai Math. J., V29, P58
[5] Baishya KK, 2021, REP MATH PHYS, V87, P407
[6] Bejan C.L., 2005, Kodai Math. J., V28, P131, DOI [10.2996/kmj/1111588042, DOI 10.2996/KMJ/1111588042]
[7] Lightlike singular hypersurfaces in quadratic gravity
Berezin, Victor A.
Ivanova, Inna D.
[J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS D, 2022, 31 (10):
[8] Constant Mean Curvature Spacelike Surfaces in Three-Dimensional Generalized Robertson-Walker Spacetimes
Caballero, Magdalena
Romero, Alfonso
Rubio, Rafael M.
[J]. LETTERS IN MATHEMATICAL PHYSICS, 2010, 93 (01) : 85 - 105
[9] Casorati F., 1890, ACTA MATH, V14, P95, DOI DOI 10.1007/BF02413317
[10] Characterizations of Lorentzian manifolds
Chaubey, S. K.
Suh, Y. J.
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2022, 63 (06)

← 1 2 3 4 5 6 →