Kodai Mathematical Journal

Ln/2-pinching theorem for submanifolds in a sphere

Huiqun Xu

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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.

Article information

Source
Kodai Math. J., Volume 30, Number 2 (2007), 246-251.

Dates
First available in Project Euclid: 3 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1183475515

Digital Object Identifier
doi:10.2996/kmj/1183475515

Mathematical Reviews number (MathSciNet)
MR2343421

Citation

Xu, Huiqun. L n /2 -pinching theorem for submanifolds in a sphere. Kodai Math. J. 30 (2007), no. 2, 246--251. doi:10.2996/kmj/1183475515. https://projecteuclid.org/euclid.kmj/1183475515


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