| 具有负数量曲率的紧致黎曼流形的Killing向量场 |
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| 引用本文： | 付海平,但萍萍,彭晓芸.具有负数量曲率的紧致黎曼流形的Killing向量场[J].数学杂志,2017,37(6):1118-1124. |
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| 作者姓名： | 付海平 但萍萍 彭晓芸 |
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| 作者单位： | 南昌大学数学系, 江西 南昌 330031,南昌大学数学系, 江西 南昌 330031,江西省税务干部学校, 江西 南昌 330029 |
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| 基金项目： | Supported by the National Natural Science Foundations of China (11261038; 11361041). |
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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.
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| 关 键 词： | Killing向量场 负数量曲率 无迹Ricci曲率张量 |
| 收稿时间： | 2016/9/2 0:00:00 |
| 修稿时间： | 2016/11/17 0:00:00 |
KILLING VECTOR FIELDS ON COMPACT RIEMANNIAN MANIFOLDS WITH NEGATIVE SCALAR CURVATURE |
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| FU Hai-ping,DAN Ping-ping and PENG Xiao-yun.KILLING VECTOR FIELDS ON COMPACT RIEMANNIAN MANIFOLDS WITH NEGATIVE SCALAR CURVATURE[J].Journal of Mathematics,2017,37(6):1118-1124. |
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| Authors: | FU Hai-ping DAN Ping-ping and PENG Xiao-yun |
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| Institution: | Department of Mathematics, Nanchang University, Nanchang 330031, China,Department of Mathematics, Nanchang University, Nanchang 330031, China and Jiangxi Tax Cadre School, Nanchang 330029, China |
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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 to6]. |
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| Keywords: | killing vector field negative scalar curvature trace-free Ricci curvature tensor |
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