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具有负数量曲率的紧致黎曼流形的Killing向量场
付海平¹, 但萍萍¹, 彭晓芸²
1.南昌大学数学系, 江西南昌 330031;2.江西省税务干部学校, 江西南昌 330029

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).

KILLING VECTOR FIELDS ON COMPACT RIEMANNIAN MANIFOLDS WITH NEGATIVE SCALAR CURVATURE

FU Hai-ping¹, DAN Ping-ping¹, PENG Xiao-yun²

1.Department of Mathematics, Nanchang University, Nanchang 330031, China;2.Jiangxi Tax Cadre School, Nanchang 330029, China

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