Chinese Quarterly Journal of Mathematics ›› 2016, Vol. 31 ›› Issue (3): 298-306.doi: 10.13371/j.cnki.chin.q.j.m.2016.03.008

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On Complete Submanifolds in Space Forms

  

  1. School of Mathematics and Statistics,Jiangsu Normal University
  • Received:2015-06-10 Online:2016-09-30 Published:2020-11-05
  • About author:ZHANG Yun-tao(1972-), male, native of Linyi, Shandong, an associate professor of Jiangsu Normal University, Ph.D., engages in di®erential geometry.
  • Supported by:
    Supported by the National Natural Science Foundation of China(11071206); Supported by the PAPD of Jiangsu Higher Education Institutions;

Abstract: Let Mn be an n(n≥4)-dimensional compact oriented submanifold in the nonnegative space forms Nn+p(c) with S ≤ S(c,H).Then Mn is either homeomorphic to a standard n-dimensional sphere Sn or isometric to a Clifford torus.We also prove that a2 xt-2compact oriented submanifold in any Nn+p(c) is diffeomorphic to a sphere if S ≤(n2H2)/(n-1)+2c. 

Key words: submanifolds, principle curvature, Ricci curvature

CLC Number: