论 GRW 时空中屏幕同调类光超曲面的一些基本曲率不变量

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2024-04-19 DOI:10.1016/j.difgeo.2024.102140

Idrees Fayaz Harry , Mehraj Ahmad Lone , Alina-Daniela Vîlcu , Gabriel-Eduard Vîlcu

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引用次数: 0

摘要

本研究的重点是广义罗伯逊-沃克（GRW）时空的类光超曲面。最近，Poyraz（2022）[51], [52]建立了一些基本不等式，涉及 GRW 时空的屏幕同调类光超曲面的各种曲率不变量，如 k-标量曲率和 k-里奇曲率。在这项工作中，我们考虑了其他基本曲率不变量，即标量曲率和 δ-Casorati 曲率，并推导出了 GRW 时空这类超曲面的新不等式。我们还找到了这些不等式中相等情况成立的条件，并给出了洛伦兹几何中的一些应用。

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

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 δ-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.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.