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 $S^4$.
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机译：在本文中，我们讨论了局部对称黎曼流形中具有闭合截面曲率的闭合最小子流形的刚度现象。我们证明，如果子流形的截面曲率不小于一个明确给定的常数，则子流形完全是测地线，或者周围空间是一个球体，并且子流形与两个球体或Veronese曲面的乘积等距。 $ S ^ 4 $。
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