Introduction to M�bius Differential Geometry
(Book #300 in the London Mathematical Society Lecture Note Series)
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This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for M?bius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed. Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers.
Format:Paperback
Language:English
ISBN:0521535697
ISBN13:9780521535694
Release Date:August 2003
Publisher:Cambridge University Press
Length:428 Pages
Weight:1.29 lbs.
Dimensions:0.8" x 6.2" x 9.0"
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