Let Mn（n ≥ 4） be an oriented closed submanifold with parallel mean curvature in an （n ＋ p）-dimensional locally symmetric Riemannian manifold Nn＋p. We prove that if the sectional curvature of N is positively pin...Let Mn（n ≥ 4） be an oriented closed submanifold with parallel mean curvature in an （n ＋ p）-dimensional locally symmetric Riemannian manifold Nn＋p. We prove that if the sectional curvature of N is positively pinched in [5, 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].展开更多
基金Supported by the National Natural Science Foundation of China(11531012,11371315,11301476)the TransCentury Training Programme Foundation for Talents by the Ministry of Education of Chinathe Postdoctoral Science Foundation of Zhejiang Province(Bsh1202060)
文摘Let Mn（n ≥ 4） be an oriented closed submanifold with parallel mean curvature in an （n ＋ p）-dimensional locally symmetric Riemannian manifold Nn＋p. We prove that if the sectional curvature of N is positively pinched in [5, 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].
