径向截面曲率有下界黎曼流形的微分同胚定理

数学物理学报 ›› 2014, Vol. 34 ›› Issue (4): 992-998.

径向截面曲率有下界黎曼流形的微分同胚定理

谢治琦¹|吴传喜²|李光汉^2*

1.首都师范大学数学科学学院北京 100048;
2.湖北大学数学与统计学学院武汉 430062

收稿日期:2013-01-08 修回日期:2013-12-20 出版日期:2014-08-25 发布日期:2014-08-25
通讯作者: 李光汉，liguanghan@163.com E-mail:zhiqi219@126.com; cxwu@hubu.edu.cn; liguanghan@163.com
基金资助:
国家自然科学基金(11171096)、教育部博士点基金(20104208110002)和武汉市学科带头人计划项目(Z201051730002)资助.

Diffeomorphic Theorems for Open Riemannian Manifolds with Radial Curvature Bounded Below

XIE Zhi-Qi¹, WU Chuan-Xi², LI Guang-Han^2*

1.School of Mathematical Science, Capital Normal University, Beijing 100048;
2.School of Mathematics and Statistics, Hubei University, Wuhan 430062

Received:2013-01-08 Revised:2013-12-20 Online:2014-08-25 Published:2014-08-25
Contact: LI Guang-Han，liguanghan@163.com E-mail:zhiqi219@126.com; cxwu@hubu.edu.cn; liguanghan@163.com
Supported by:
国家自然科学基金(11171096)、教育部博士点基金(20104208110002)和武汉市学科带头人计划项目(Z201051730002)资助.

摘要/Abstract

摘要：

研究了径向截面曲率以一类旋转模曲面的Gauss曲率为下界的非紧完备黎曼流形的拓扑, 得到了该类黎曼流形与欧氏空间微分同胚的一个合理的充分条件, 推广了径向截面曲率有常数下界完备黎曼流形的微分同胚定理.

关键词: 微分同胚, 径向截面曲率, 模曲面

Abstract:

In this paper, we study complete non-compact Riemannian manifolds with radial curvature bounded from below by that of a non-compact model surface of revolution. We find a reasonable condition to ensure that this kind of manifolds are diffeomorphic to a Euclidean space if it contains enough rays starting from the base point.

Key words: Diffeomorphic theorem, Radial curvature, Model surface

中图分类号:

53C20

谢治琦, 吴传喜, 李光汉. 径向截面曲率有下界黎曼流形的微分同胚定理[J]. 数学物理学报, 2014, 34(4): 992-998.

XIE Zhi-Qi, WU Chuan-Xi, LI Guang-Han. Diffeomorphic Theorems for Open Riemannian Manifolds with Radial Curvature Bounded Below[J]. Acta mathematica scientia,Series A, 2014, 34(4): 992-998.

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