On integral formulas for submanifolds of spaces of constant curvature and some applications (Q760924)

The article is concerned with integral formulas of Minkowski type for compact oriented submanifolds of a space of constant curvature with arbitrary codimension. In the integrand higher mean curvatures (defined as multilinear forms on the normal bundle), a conformal vector field along the submanifold and parallel normal vector fields are involved. The main results include formulas of several other authors. Applications: a generalization of the Liebmann-Süss theorem, upper bounds for the first eigenvalue of the Laplace operator of the submanifold.