Harmonic morphisms between Riemannian manifolds

Format Post in Mathematics BY John C. Wood, Paul Baird

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Harmonic morphisms between Riemannian manifolds
John C.Harmonic morphisms between Riemannian ... Textbook Wood, Paul Baird
Type: eBook
Released: 2003
Publisher: OUP
Page Count: 534
Format: djvu
Language: English
ISBN-10: 0198503628
ISBN-13: 9780198503620
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 conepts in differential geometry, for example, Killing fields, geodesics, foliations, Clifford systems, twistor spaces, Hermitian structures, iso-parametric mappings, and Einstein metrics and also the Brownain pathpreserving maps of probability theory. Giving a complete account of the fundamental aspects of the subject, this book is self-contained, assuming only a basic knowledge of differential geometry.

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