关于弱伸展的克罗皮纳度量

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2024-02-21 DOI:10.1016/j.difgeo.2024.102118

A. Tayebi, F. Barati

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引用次数: 0

摘要

在本文中，我们研究了弱拉伸克罗皮纳度量，并证明了一个刚性定理。我们证明了弱拉伸克罗皮纳度量的相关单形式相对于相关黎曼度量是保角基林的。我们发现任何弱拉伸克罗皮纳度量都有消失的 S 曲率。然后，我们证明每个弱拉伸克罗皮纳度量都是贝沃德度量。事实证明，每一个 R-quadratic Kropina 公设都是 Berwald 公设。最后，我们证明当且仅当每个正完全 C 可简公设是贝瓦尔德公设时，它才是 R 四元公设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On weakly stretch Kropina metrics

In this paper, we study weakly stretch Kropina metrics and prove a rigidity theorem. We show that the associated one-form of a weakly stretch Kropina metric is conformally Killing with respect to the associated Riemannian metric. We find that any weakly stretch Kropina metric has vanishing S-curvature. Then, we prove that every weakly stretch Kropina metric is a Berwald metric. It turns out that every R-quadratic Kropina metric is a Berwald metric. Finally, we show that every positively complete C-reducible metric is R-quadratic if and only if it is Berwaldian.

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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.