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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, 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.
This text investigates the mathematical theory of harmonic morphisms, specifically focusing on maps between Riemannian manifolds that preserve Laplace's equation. Authors John C. Wood and Paul Baird provide a comprehensive, self-contained framework for understanding these maps, which are characterized as harmonic maps satisfying a specific first-order condition. The book synthesizes foundational definitions with advanced applications, drawing upon the authors' expertise in differential geometry to bridge the gap between theoretical constructs and practical geometric analysis.
What You Will Find
Experts recognize this monograph as a foundational text for researchers and graduate students specializing in differential geometry. Readers frequently note the technical density of the prose, which requires a solid background in manifold theory to fully grasp the presented proofs and applications.
Page Count:
536
Publication Date:
2003-05-29
Publisher:
Oxford University Press
ISBN-10:
0198503628
ISBN-13:
9780198503620
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