Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2013; 50(1): 135-142

Printed January 31, 2013

https://doi.org/10.4134/BKMS.2013.50.1.135

Copyright © The Korean Mathematical Society.

The rigidity of minimal submanifolds in a locally symmetric space

Shunjuan Cao

Zhejiang Agricultural and Forestry University

Abstract

In the present paper, we discuss the rigidityphenomenon of closed minimal submanifolds in a locally symmetric Riemannian manifold with pinched sectional curvature. We show that if the sectional curvature of the submanifold is no less than an explicitly given constant, then either the submanifold is totally geodesic, or the ambient space is a sphere and the submanifold is isometric to a product of two spheres or the Veronese surface in $S^4$.

Keywords: minimal submanifold, rigidity, sectional curvature, locally symmetric space

MSC numbers: 53C24, 53C40