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Generalized Minkowski formulae for compact submanifolds of a Riemannian manifold

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Geoffrey Howard Smith
Geoffrey Howard Smith
Affiliation:
The School of Mathematical Sciences, The N.S.W. Institute of TechnologyP.O. Box 123 Broadway, N.S.W. 2007Australia
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Abstract

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In 1903 H. Minkowski obtained two integral formulae for closed convex surfaces in three dimensional Euclidean space. In this paper we obtain generalised Minkowski formulae on compact orientable immersed submanifolds of an arbitrary Riemannian manifold. By successive specialisation we indicate how known integral theorems can be obtained as particular cases of our result.

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53C40: Global submanifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 3 , June 1984 , pp. 378 - 388
Copyright
Copyright © Australian Mathematical Society 1984

References

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