On integral formulas for submanifolds of spaces of constant curvature and some applications

Abstract

Integral formulas of Minkowski type, involving the higher mean curvatures as multilinear forms on the normal bundle, are proved for compact oriented immersed submanifolds with arbitrary codimension in a Riemannian manifold of constant curvature, and as application a generalization of the Liebmann-Suss theorem as well as upper bounds for the first positive eigenvalue of the Laplace operator are given.