一类芬斯勒空间的共形向量场

Pub Date : 2024-07-07 DOI:10.1007/s10998-024-00594-1

Guojun Yang

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引用次数: 0

摘要

在本文中，我们首先给出了两个基本原理来表征 \((\alpha ,\beta )\) 空间的共形向量场是同调的，并确定了这些同调场的局部结构。然后，我们利用这些原理来研究在一定曲率条件下的（(\alpha ,\beta)）空间的共形向量场。此外，我们还在一系列局部投影平坦的兰德斯空间上构造了非同调共形向量场。

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Conformal vector fields of a class of Finsler spaces

In this paper, we first give two fundamental principles to characterize conformal vector fields of \((\alpha ,\beta )\)-spaces to be homothetic and determine the local structure of those homothetic fields. Then we use the principles to study conformal vector fields of \((\alpha ,\beta )\)-spaces under certain curvature conditions. Besides, we construct a family of non-homothetic conformal vector fields on a family of locally projectively flat Randers spaces.

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