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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 115-119.doi: 10.6040/j.issn.1671-9352.0.2018.604

• • 上一篇    

完备非紧黎曼流形的基本群

陈爱云1,薛琼1*,肖小峰2   

  1. 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
  • 发布日期:2019-12-11
  • 作者简介:陈爱云(1993— ),女,硕士研究生,研究方向为微分几何及应用. E-mail:1113603226@qq.com*通信作者简介:薛琼(1980— ),女,博士,副教授,研究方向为微分几何及应用. E-mail:rabbit_801005@163.com
  • 基金资助:
    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)

On the fundamental group of complete noncompact Riemannian manifolds

CHEN Ai-yun1, XUE Qiong1*, XIAO Xiao-feng2   

  1. 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
  • Published:2019-12-11

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

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.

中图分类号: 

  • O186
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[1] 陈爱云,薛琼,陈欢欢,肖小峰. 具有渐近非负Ricci曲率完备非紧的黎曼流形[J]. 山东大学学报(理学版), 2018, 53(4): 1-6.
[2] 何超,李影,宋卫东. 局部对称伪黎曼流形中的2-调和类时子流形[J]. 山东大学学报(理学版), 2016, 51(10): 54-58.
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