Killing vector fields on compact Finsler manifolds
Killing vector fields on compact Finsler manifolds
复制标题
紧凑芬斯勒流形上的消杀矢量场
DOI：
10.5486/pmd.2016.6039
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Tongde Zhong
中科院分区：
文献类型：
--
作者：
Jinling Li;Chunhui Qiu;Tongde Zhong
本文得到了紧致Finsler流形上Killing向量场的Weitzenbock型公式。利用“Bochner技巧”，证明了Killing向量场在一定曲率条件和其它附加条件下是平行的或同零的。特别地，我们讨论了某些紧的特殊Finsler流形上的Killing向量场.证明了Minkowski空间中独立Killing向量场的个数等于Minkowski空间的维数。
In this paper, we obtain the Weitzenbock type formula for Killing vector fields on a compact Finsler manifold. By using the "Bochner technique", we prove that Killing vector fields are parallel or vanish identically under certain curvature condition and other extra condition. In particular, we discuss Killing vector fields on some compact special Finsler manifolds. Moreover, we prove that the number of the independent Killing vector fields in a Minkowskian space is equal to the dimension of a Minkowskian space.