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Harmonic Morphisms Between Riemannian Manifolds
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Harmonic Morphisms Between Riemannian Manifolds

Paul Baird and John C. Wood

Abstract

Harmonic morphisms are maps which preserve Laplace's equation. More explicitly, a map between Riemannian manifolds is called a harmonic morphism if its composition with any locally defined harmonic function on the codomain is a harmonic function on the domain; it thus ‘pulls back’ germs of harmonic functions to germs of harmonic functions. Harmonic morphisms can be characterized as harmonic maps satisfying a condition dual to weak conformality called ‘horizontal weak conformality’ or ‘semiconformality’. Examples include harmonic functions, conformal mappings in the plane, holomorphic mappings ... More

Keywords: harmonic map, Laplace's equation, conformal, Killing field, twistor, foliation

Bibliographic Information

Print publication date: 2003 Print ISBN-13: 9780198503620
Published to Oxford Scholarship Online: September 2007 DOI:10.1093/acprof:oso/9780198503620.001.0001

Authors

Affiliations are at time of print publication.

Paul Baird, author
Professeur de Mathématiques, Université de Bretagne Occidentale, Brest

John C. Wood, author
Professor of Pure Mathematics, University of Leeds

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