数学季刊 ›› 2007, Vol. 22 ›› Issue (1): 16-21.

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小Excess与具负下界Ricci曲率开流行的拓扑

  

  1. Small Excess andSchool of Mathematics and Statistics,Huazhong Normal University,Wuhan 430079,China
  • 收稿日期:2004-04-07 出版日期:2007-03-30 发布日期:2023-11-10
  • 作者简介:XU Sen-lin(1941-),male,native of Xuzhou,Jiangsu,a professor of Huazhong Normal Univer- sity,Ph.D.,engages in global differential geoinetry;HU Zi-sheng(1980-),male,native of Suizhou,Hubei,Ph.D., engages in global differential geometry.
  • 基金资助:
     Supported by the National Natural Science Foundation of China(10371047);

Small Excess and the Topology of Open Manifolds with Ricci Curvature Negatively Lower Bounded

  1. Small Excess andSchool of Mathematics and Statistics,Huazhong Normal University,Wuhan 430079,China
  • Received:2004-04-07 Online:2007-03-30 Published:2023-11-10
  • About author:XU Sen-lin(1941-),male,native of Xuzhou,Jiangsu,a professor of Huazhong Normal Univer- sity,Ph.D.,engages in global differential geoinetry;HU Zi-sheng(1980-),male,native of Suizhou,Hubei,Ph.D., engages in global differential geometry.
  • Supported by:
     Supported by the National Natural Science Foundation of China(10371047);

摘要: In this paper,we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry.We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius,which improves some results in [4].

关键词: open manifolds, Ricci curvature, conjugate radius, critical point, Excess func- tion, triangle comparison theorems

Abstract: In this paper,we study the relation between the excess of open manifolds and their topology by using the methods of comparison geometry.We prove that a complete open Riemmannian manifold with Ricci curvature negatively lower bounded is of finite topological type provided that the conjugate radius is bounded from below by a positive constant and its Excess is bounded by some function of its conjugate radius,which improves some results in [4].

Key words: open manifolds, Ricci curvature, conjugate radius, critical point, Excess func- tion, triangle comparison theorems

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