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A characterisation of Riemannian foliations and totally umbilical submanifolds

Published online by Cambridge University Press:  17 April 2009

Ph. Tondeur  and
L. Vanhecke
Ph. Tondeur
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana Il. 61801, United States of America
L. Vanhecke
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B B-3001 Leuven, Belgium
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We discuss characterisations of Riemannian foliations, totally geodesic submanifolds, and totally umbilical submanifolds by sharp inequalities. These derive from the same linear algebraic set up, characterising a linear endomorphism which is a multiple of the identity.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 48 , Issue 1 , August 1993 , pp. 101 - 108
Copyright
Copyright © Australian Mathematical Society 1993

References

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