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Conformal variation of a hypersurface of constant mean curvature in an einstein space

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Geoffrey Howard Smith
Geoffrey Howard Smith
Affiliation:
The New South Wales Institute of TechnologyP. O. Box 123 Broadway, New South Wales 2007, Australia
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Abstract

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Let a compact orientable manifold be immersed as a hypersurface of constant mean curvature in an Einstein space. It is shown that the immersion is totally umbilical if and only if there exists a conformal variation of the immersion whose variation vector is nowhere tangential to the hypersurface.

MSC classification

Secondary: 53C42: Immersions (minimal, prescribed curvature, tight, etc.) 53C40: Global submanifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 229 - 234
Copyright
Copyright © Australian Mathematical Society 1982

References

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Liebmann, H. (1900), ‘Über die Verbiegung der geschlossenen Flächen positiver Krümmung’, Math. Ann. 53, 91–112.Google Scholar