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Harmonic Morphisms Between Riemannian Manifolds
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Harmonic Morphisms Between Riemannian Manifolds

Paul Baird and John C. Wood


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


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