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Harmonic Morphisms Between Riemannian Manifolds$
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Paul Baird and John C. Wood

Print publication date: 2003

Print ISBN-13: 9780198503620

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198503620.001.0001

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Fundamental properties of harmonic morphisms

Fundamental properties of harmonic morphisms

(p.106) 4 Fundamental properties of harmonic morphisms
Harmonic Morphisms Between Riemannian Manifolds

Paul Baird

John C. Wood

Oxford University Press

This chapter characterizes harmonic morphisms between Riemannian manifolds and discusses their basic properties. The first non-constant term of the Taylor series of a harmonic morphism at a point called ‘symbol’ is considered. The tension field of a submersion is related to the mean curvature of the fibres, yielding geometrical criteria for harmonic morphisms that leads to a study of the associated foliations. The chapter concludes with a discussion of the second variation of energy and volume.

Keywords:   symbol, mean curvature, minimal fibres, foliation, second variation

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