Hadamard-Frankel type theorems for manifolds with partially positive curvature.
Hadamard-Frankel type theorems for manifolds with partially positive curvature.
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DOI：
10.2140/pjm.1996.176.129
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发表时间：
1996-11
影响因子：
0.6
通讯作者：
K. Kenmotsu;C. Xia
中科院分区：
文献类型：
--
作者：
K. Kenmotsu;C. Xia
本文证明了一些定理：满足部分正曲率黎曼流形或部分正全纯截面曲率凯勒流形中子流形维数条件的两个最小子流形必须相交。我们的结果表明，关于具有正曲率的流形中最小子流形的交集的著名弗兰克尔定理可以推广到非常广泛的具有部分正曲率的流形类别。
In this paper we prove some theorems that two minimal submanifolds satisfying a condition for the dimensions of the submanifolds in a Riemannian manifolds with partially positive curvature or a Kaehler manifold with partially positive holomorphic sectional curvature must intersect. Our results show that the famous Frankel theorem about intersections of minimal submanifolds in a manifold with positive curvature is generalized to the very wide class of manifolds with partially positive curvature.