Readership: Graduate students and researchers of mathematics (differential geometry and Brownian Motion).
Paul Baird, Professeur de Mathématiques, Université de Bretagne Occidentale, Brest, and John C. Wood, Professor of Pure Mathematics, University of Leeds
"The book is written by two of the foremost experts on harmonic maps and harmonic morphisms. Serious dedication and commitment to the quality and scope of the work have resulted in this veritable opus. The exposition is lucid and authorative, making it a highly enjoyable reading, as well as a powerful reference tool." - Bulletin London Math Society Vol 38, 2006
"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." - Sigmundur Gudmundsson and Martin Svensson, Finite Packing and Covering
Introduction IBasic Facts on Harmonic Morphisms 1: Complex-valued harmonic morphisms on three-dimensional Euclidean space 2: Riemannian manifolds and conformality 3: Harmonic mappings between Riemannian manifolds 4: Fundamental properties of harmonic morphisms 5: Harmonic morphisms defined by polynomials IITwistor Methods 6: Mini-twistor theory on three-dimensional space-forms 7: Twistor methods 8: Holomorphic harmonic morphisms 9: Multivalued harmonic morphisms IIITopological and Curvature considerations 10: Harmonic morphisms from compact 3-manifolds 11: Curvature considerations 12: Harmonic morphisms with one-dimensional fibres 13: Reduction techniques IVFurther Developments 14: Harmonic morphisms between semi-Riemannian manifolds Appendix Glossary of Notation Bibliography Index
