共形向量场与若干刚性定理

数学物理学报 ›› 2017, Vol. 37 ›› Issue (4): 615-623.

共形向量场与若干刚性定理

黄琴¹, 阮其华¹, 陈凡²

1 莆田学院数学学院福建莆田 351100;
2 闽南师范大学数学与统计学院福建漳州 363000

收稿日期:2016-11-28 修回日期:2017-04-19 出版日期:2017-08-26 发布日期:2017-08-26
通讯作者: 阮其华,E-mail:ruanqihua@163.com E-mail:ruanqihua@163.com
基金资助:
国家自然科学基金（11471175）、福建省自然科学基金（2016J01675）和福建省教育厅科技项目（JTA160448）

Conformal Vector Fields and Some Rigidity Theorems

Huang Qin¹, Ruan Qihua¹, Chen Fan²

1 School of Mathematics, Putian University, Fujian Putian 351100;
2 Department of Mathematics, Minnan Normal University, Fujian Zhangzhou 363000

Received:2016-11-28 Revised:2017-04-19 Online:2017-08-26 Published:2017-08-26
Supported by:
Supported by NSFC (11471175), the Natural Science Foundation of Fujian Province (2016J01675) and the Fund of Department of Education of Fujian Province (JTA160448)

摘要/Abstract

摘要： 该文讨论了某一类特殊流形的形状问题，即当某些紧的黎曼流形上存在一个非平凡的共形向量场且数量曲率为常数时，研究在什么情况下该流形等距于欧式空间中的球面.另外还研究当黎曼流形的数量曲率是非常数时相应的若干刚性定理.

关键词: 共形向量场, 刚性定理, 数量曲率, 修正的里奇张量

Abstract: In this paper, we discuss a question about what condition can enforce a compact Riemannian manifold carrying a nontrivial conformal vector field and with a constant scalar curvature to be isometric to an Euclidean sphere. We also study a Riemannian manifold with nonconstant scalar curvature and obtain some corresponding rigidity theorems.

Key words: Conformal vector field, Rigidity theorem, Scalar curvature, Modified Ricci tensor

中图分类号:

O186.1

黄琴, 阮其华, 陈凡. 共形向量场与若干刚性定理[J]. 数学物理学报, 2017, 37(4): 615-623.

Huang Qin, Ruan Qihua, Chen Fan. Conformal Vector Fields and Some Rigidity Theorems[J]. Acta mathematica scientia,Series A, 2017, 37(4): 615-623.

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