Geometriae Dedicata

, Volume 45, Issue 1, pp 83–88

Rigidity of compact minimal submanifolds in a unit sphere

  • Qing Chen
  • Senlin Xu
Article

DOI: 10.1007/BF01667404

Cite this article as:
Chen, Q. & Xu, S. Geom Dedicata (1993) 45: 83. doi:10.1007/BF01667404

Abstract

LetM be ann-dimensional compact minimal submanifold of a unit sphereSn+p (p≥2); and letS be a square of the length of the second fundamental form. IfS≤2/3n everywhere onM, thenM must be totally geodesic or a Veronese surface.

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Qing Chen
    • 1
  • Senlin Xu
    • 1
  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefeiPeople's Republic of China