Harmonic Morphisms Between Riemannian Manifolds

ISBN-13: 9780198503620 / Angielski / Twarda / 2003 / 536 str.

Paul Baird; John C. Wood; P. Baird

Opis

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, 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.

Recenzje

This informative and inspiring book gathers the most important results on harmonic morpisms into a single volume, presenting them in a unified and modern way.