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Submanifolds and the length of the second fundamental tensor

Part of: Global differential geometry

Published online by Cambridge University Press:  09 April 2009

Thomas Hasanis
Thomas Hasanis
Affiliation:
Department of Mathematics University of IoanninaIoannina, Greece
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Abstract

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A sufficient condition, for a complete submanifold of a Riemannian manifold of positive constant curvature to be umbilical, is given. The condition will be given by an inequality which is established between the length of the second fundamental tensor and the mean curvature.

Keywords

second fundamental tensortotally umbilical submanifolds.

MSC classification

Secondary: 53C40: Global submanifolds
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 1 , February 1983 , pp. 1 - 6
Copyright
Copyright © Australian Mathematical Society 1983

References

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[5]Hasanis, Th., ‘Submanifolds and a pinching problem on the second fundamental tensors’, to appear.Google Scholar
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