| 完备非紧黎曼流形的基本群 |
| |
| 引用本文： | 陈爱云,薛琼,肖小峰. 完备非紧黎曼流形的基本群[J]. 山东大学学报(理学版), 2019, 54(12): 115-119. DOI: 10.6040/j.issn.1671-9352.0.2018.604 |
| |
| 作者姓名： | 陈爱云 薛琼 肖小峰 |
| |
| 作者单位： | 1.武汉理工大学理学院, 湖北 武汉 430070;2.武汉纺织大学机械工程与自动化学院, 湖北 武汉 430073 |
| |
| 基金项目： | 国家自然科学基金资助项目(61573012);中央高校基本科研业务费专项资金资助项目(2017IA006) |
| |
| 摘 要： | 研究了一类完备非紧的n维黎曼流形,Ricci曲率满足RicM≥-(n-1)k(k>0),利用点到极小测地圈中点的距离的一致估计,证明了此流形在满足小的直径线性增长条件下,其基本群是有限生成的。
|
| 关 键 词： | 黎曼流形 Ricci曲率 小的直径线性增长 基本群 |
On the fundamental group of complete noncompact Riemannian manifolds |
| |
| CHEN Ai-yun,XUE Qiong,XIAO Xiao-feng. On the fundamental group of complete noncompact Riemannian manifolds[J]. Journal of Shandong University, 2019, 54(12): 115-119. DOI: 10.6040/j.issn.1671-9352.0.2018.604 |
| |
| Authors: | CHEN Ai-yun XUE Qiong XIAO Xiao-feng |
| |
| Affiliation: | 1. School of Science, Wuhan University of Technology, Wuhan 430070, Hubei, China; 2. School of Mechanical Engineering and Automation, Wuhan Textile University, Wuhan 430073, Hubei, China |
| |
| Abstract: | We study the topology of complete noncompact Riemannian manifolds with Ricci curvature satisfies RicM≥-(n-1)k(k>0). By using the uniform estimates for the distance from a point to halfway point of minimal geodesics, we prove that a manifold with linear diameter growth has a finitely generated fundamental group. |
| |
| Keywords: | |
|
| 点击此处可从《山东大学学报(理学版)》浏览原始摘要信息 |
|
点击此处可从《山东大学学报(理学版)》下载全文 |
