On integral formulas for submanifolds of spaces of constant curvature and some applications |
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Authors: | Wolf Strübing |
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Institution: | (1) Institut für Mathematik, Universität Dortmund, D-4600 Dortmund 50, Federal Republic of Germany |
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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-Süss theorem as well as upper bounds for the first positive eigenvalue of the Laplace operator are given. |
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