Submanifolds with parallel mean curvature vector in pinched Riemannian manifolds

F. Fontenele

Vol. 177 (1997), No. 1, 47–70

DOI: 10.2140/pjm.1997.177.47

Abstract

In this paper, we prove a generalized integral inequality for submanifolds with parallel mean curvature vector in an arbitrary Riemannian manifold, and from which we obtain a pinching theorem for compact oriented submanifolds with parallel mean curvature vector in a complete simply connected pinched Riemannian manifold, which generalizes the results obtained by Alencar-do Carmo and Hong-Wei Xu.

Milestones

Received: 22 March 1995

Published: 1 January 1997