准爱因斯坦流形承认闭合共形矢量场

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2023-11-24 DOI:10.1016/j.difgeo.2023.102083

J.F. Silva Filho

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引用次数: 0

摘要

本文研究了具有闭共形向量场的拟爱因斯坦流形。首先给出了带非平行闭共形矢量场的常标量曲率拟爱因斯坦流形的刚性结果。此外，我们还证明了具有闭共形向量场的拟爱因斯坦流形几乎在任何地方都可以共形化为常数标量曲率。最后，我们得到了具有非平行梯度共形向量场的拟爱因斯坦流形的一个表征。

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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Quasi-Einstein manifolds admitting a closed conformal vector field

In this article, we investigate quasi-Einstein manifolds admitting a closed conformal vector field. Initially, we present a rigidity result for quasi-Einstein manifolds with constant scalar curvature and carrying a non-parallel closed conformal vector field. Moreover, we prove that quasi-Einstein manifolds admitting a closed conformal vector field can be conformally changed to constant scalar curvature almost everywhere. Finally, we obtain a characterization for quasi-Einstein manifolds endowed with a non-parallel gradient conformal vector field.

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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.