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.
Shunjuan Cao
Zhejiang Agricultural and Forestry University
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
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