JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (4): 1-6.doi: 10.6040/j.issn.1671-9352.0.2017.480

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Complete noncompact Riemannian manifold with asymptotically nonnegative Ricci curvature

CHEN Ai-yun1, XUE Qiong1*, CHEN Huan-huan1, 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
  • Received:2017-09-22 Online:2018-04-20 Published:2018-04-13

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Abstract: We study the topology of complete noncompact Riemannian manifolds with asymptotically nonnegative Ricci curvature. By using extensions of Excess function and Busemann function, it is proved that they have finite topological type under sectional curvature bounded from nonnegative below kp(r)≥- C/((1+r)α) and large volume growth, which extend a series known results.

Key words: asymptotically nonnegative Ricci curvature, Busemann function, finite topological type, Excess function, large volume growth

CLC Number: 

  • O186
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