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Harmonicity of a foliation and of an associated map

Published online by Cambridge University Press:  17 April 2009

Philippe Tondeur  and
Lieven Vanhecke
Philippe Tondeur
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, II 61801, United States of America
Lieven Vanhecke
Affiliation:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3001 Leuven, Belgium
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Abstract

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A foliation on a Riemannian manifold (M, g) is harmonic if all the leaves are minimal submanifolds. We give a new characterisation of the harmonicity of a foliation on (M, g) by the harmonicity of an associated bundle map of (T M, gC), where gC is the complete lift metric of g to the tangent bundle as introduced by Yano and Ishihara.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 2 , October 1996 , pp. 241 - 246
Copyright
Copyright © Australian Mathematical Society 1996

References

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