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

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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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  1. Institut für Mathematik, Universität Dortmund, D-4600, Dortmund 50, Federal Republic of Germany

    Wolf Strübing

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  1. Wolf Strübing
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Strübing, W. On integral formulas for submanifolds of spaces of constant curvature and some applications. Manuscripta Math 49, 177–194 (1984). https://doi.org/10.1007/BF01168750

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