THE RIGIDITY OF MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC SPACE

Title & Authors
THE RIGIDITY OF MINIMAL SUBMANIFOLDS IN A LOCALLY SYMMETRIC SPACE
Cao, Shunjuan;

Abstract
In the present paper, we discuss the rigidity phenomenon 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 $\small{S^4}$.
Keywords
minimal submanifold;rigidity;sectional curvature;locally symmetric space;
Language
English
Cited by
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