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Mean Curvature of Riemannian Foliations

Published online by Cambridge University Press:  20 November 2018

Peter March ,
Maung Min-Oo  and
Ernst A. Ruh
Peter March
Affiliation:
Department of Mathematics, The Ohio State University, Columbus OH 43210, U.S.A.
Maung Min-Oo
Affiliation:
Math. Inst., Univ. Fribourg, Chemin du Musee 23, CH-1700 Fribourg, Switzerland
Ernst A. Ruh
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada L8S 4K1
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Abstract

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It is shown that a suitable conformai change of the metric in the leaf direction of a transversally oriented Riemannian foliation on a closed manifold will make the basic component of the mean curvature harmonic. As a corollary, we deduce vanishing and finiteness theorems for Riemannian foliations without assuming the harmonicity of the basic mean curvature.

Keywords

53C1257R30
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 1 , 01 March 1996 , pp. 95 - 105
Copyright
Copyright © Canadian Mathematical Society 1995

References

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