Submanifolds with parallel mean curvature vector in pinched Riemannian manifolds (Q1816523)

We prove a generalized integral inequality for submanifolds with parallel mean curvature vectors in an arbitrary Riemannian manifold, from which we obtain a pinching theorem for compact oriented submanifolds with parallel mean curvature vectors in a complete simply connected pinched Riemannian manifold, which generalizes results obtained by M. P. do Carmo and Hong-Wei Xu [see also the author's paper of the same title in An. Acad. Bras. Cienc. 67, No. 3, 283-287 (1995; Zbl 0857.53037).].