Hadamard-Frankel type theorems for manifolds with partially positive curvature

Katsuei Kenmotsu and Changyu Xia

Vol. 176 (1996), No. 1, 129–139

DOI: 10.2140/pjm.1996.176.129

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.

Mathematical Subject Classification 2000

Primary: 53C21

Secondary: 53C20

Milestones

Received: 26 May 1994

Published: 1 November 1996