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Harmonic Morphisms Between Riemannian Manifolds

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This is the first account in book form of the theory of harmonic morphisms between Riemannian manifolds. Harmonic morphisms are maps which preserve Laplace's equation. They can be characterized as harmonic maps which satisfy an additional first order condition. Examples include harmonic functions, conformal mappings in the plane, and holomorphic functions with values in a Riemann surface. There are connections with many concepts in differential geometry, for example, Killing fields, geodesics, foliations, Clifford systems, ...

Harmonic Morphisms Between Riemannian Manifolds 2003, OUP Oxford, Oxford, England

ISBN-13: 9780198503620