华东师范大学学报(自然科学版) ›› 2003, Vol. 2003 ›› Issue (2): 1-5.

• 论文 •    下一篇

相互ε-临界点球定理的一个注记

廖蔡生   

  1. 华东师范大学 数学系，上海 200062
  • 收稿日期:2001-04-02 修回日期:2001-12-03 出版日期:2003-04-15 发布日期:2003-04-15

A Remark on A Sphere Theorem with Mutually ε-critical

LIAO Cai-sheng   

  1. Department of Mathematics, East China Normal University, Shanghai 200062,China
  • Received:2001-04-02 Revised:2001-12-03 Online:2003-04-15 Published:2003-04-15

摘要： 该文利用径向曲率的Toponogov定理，证明了一个球定理：给定Λ＞0，存在一正数ε*=ε*（Λ），如果n维完备黎曼流形M包含两点p，q，满足p和q相互ε*-临界点，且d(p,q)2Kminp≥-Λ,那么M同胚于球Sn。

关键词: 咄昑珲?, Toponogo孶璚, ε-临界点, 球定理, 咄昑珲?, Toponogo孶璚, ε-临界点, 球定理

Abstract: In this note, using Toponogov theorem for adial curvature, we prove some a sphere theorem for radial curvature.

Key words: toponogov theorem, FONT-FAMILY: 宋体, mso-bidi-font-size: 12.0pt, mso-bidi-font-family: 'Times New Roman', mso-font-kerning: 1.0pt, radial curvature, toponogov theorem, FONT-FAMILY: 宋体, mso-bidi-font-size: 12.0pt, mso-bidi-font-family: 'Times New Roman', mso-font-kerning: 1.0pt