Kodai Mathematical Journal
Online ISSN : 1881-5472
Print ISSN : 0386-5991
ISSN-L : 0386-5991
Ln/2-pinching theorem for submanifolds in a sphere
Huiqun Xu
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2007 Volume 30 Issue 2 Pages 246-251

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Abstract
Let Mn (n ≥ 2) be a n-dimensional oriented closed submanifolds with parallel mean curvature in Sn + p (1), denote by S, the norm square of the second fundamental form of M. H is the constant mean curvature of M. We prove that if ∫M Sn/2A (n), where A (n) is a positive universal constant, then M must be a totally umbilical hypersurface in the sphere Sn + 1.
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© 2007 Department of Mathematics, Tokyo Institute of Technology
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