Rigidity of closed submanifolds in a locally symmetric Riemannian manifold |
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Authors: | Juan-ru Gu Yan Leng Hong-wei Xu |
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Institution: | 1.Department of Applied Mathematics,Zhejiang University of Technology,Hangzhou,China;2.Center of Mathematical Sciences,Zhejiang University,Hangzhou,China |
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Abstract: | Let M n (n ≥ 4) be an oriented closed submanifold with parallel mean curvature in an (n + p)-dimensional locally symmetric Riemannian manifold N n+p . We prove that if the sectional curvature of N is positively pinched in δ, 1], and the Ricci curvature of M satisfies a pinching condition, then M is either a totally umbilical submanifold, or δ = 1, and N is of constant curvature. This result generalizes the geometric rigidity theorem due to Xu and Gu 15]. |
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