manuscripta mathematica

, Volume 85, Issue 1, pp 79–87

Rigidity and sphere theorem for manifolds with positive Ricci curvature

  • Changyu Xia

DOI: 10.1007/BF02568185

Cite this article as:
Xia, C. Manuscripta Math (1994) 85: 79. doi:10.1007/BF02568185


LetM be a complete Riemannian manifold with Ricci curvature having a positive lower bound. In this paper, we prove some rigidity theorems forM by the existence of a nice minimal hypersurface and a sphere theorem aboutM. We also generalize a Myers theorem stating that there is no closed immersed minimal submanifolds in an open hemisphere to the case that the ambient space is a complete Riemannian manifold withk-th Ricci curvature having a positive lower bound.

1991 Mathematics Subject Classification

53C20 53C42

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Changyu Xia
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of Science and Technology of ChinaHefei, AnhuiP. R. China
  2. 2.Mathematical InstituteTohoku UniversitySendaiJapan