JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 115-119.doi: 10.6040/j.issn.1671-9352.0.2018.604

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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

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.

CLC Number: 

  • O186
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