Hadamard-Frankel type theorems for manifolds with partially positive curvature

Abstract

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.