Strongly and weakly affine vector fields on Finsler manifolds

被引：2
|
作者：
Shen, Bin [1 ]
机构：
[1] Southeast Univ, Sch Math, Nanjing 211189, Jiangsu, Peoples R China
来源：
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS | 2019年 / 62卷
关键词：
Finsler metric; Affine vector field; Ricci curvature; Bochner formula; THEOREM;
D O I：
10.1016/j.difgeo.2018.11.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the affine vector fields on both compact and forward complete Finsler manifolds. We first give definitions of the affine transformation and the affine vector field. Unexpectedly, we find two kinds of affine fields, which are named as the strongly and weakly affine vector fields. Based on these definitions, we prove some rigidity theorems of affine fields on compact and forward complete Finsler manifolds. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：190 / 211
页数：22
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