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| 摘要: |
| 本文研究了具有负数量曲率的紧致黎曼流形上的Killing向量场.利用Bochner方法，得到在此类流形上非平凡的Killing向量场的存在的必要条件.这个结果拓广了文献[6]中的定理1. |
| 关键词: Killing向量场 负数量曲率 无迹Ricci曲率张量 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:Supported by the National Natural Science Foundations of China (11261038; 11361041). |
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| KILLING VECTOR FIELDS ON COMPACT RIEMANNIAN MANIFOLDS WITH NEGATIVE SCALAR CURVATURE |
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FU Hai-ping,DAN Ping-ping,PENG Xiao-yun
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| Abstract: |
| In this paper, we investigate killing vector fields on compact Riemannian manifolds with negative scalar curvature. By using the Bochner method, we obtain a necessary condition of the existence of non-trivial killing vector fields on these manifolds, which extends Theorem 1 due to[6]. |
| Key words: killing vector field negative scalar curvature trace-free Ricci curvature tensor |
