## Kodai Mathematical Journal

### Ln/2-pinching theorem for submanifolds in a sphere

Huiqun Xu

#### 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