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Introduction to Möbius Differential Geometry (London Mathematical Society Lecture Note Series, Series Number 300) - Softcover

 
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This introduction to the conformal differential geometry of surfaces and submanifolds covers those aspects of the geometry of surfaces that only refer to an angle measurement, but not to a length measurement. Different methods (models) are presented for analysis and computation. Various applications to areas of current research are discussed, including discrete net theory and certain relations between differential geometry and integrable systems theory.

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Book Description

An introduction, at a basic level, to the conformal differential geometry of surfaces and submanifolds is given. That is, the book discusses those aspects of the geometry of surfaces that does only refer to an angle measurement but not to a length measurement. Different methods (models) to think about their geometry as well as to do computations are presented. Various applications to areas of current research interest are discussed, including discrete net theory and certain relations between differential geometry and integrable systems theory.

Review

"...carefully written with detailed references, extensive historical notes and helpful comments at the beginning of each new chapter. It is an outstanding introduction to a classical field which has taken on new life over the past quarter century, and it is highly recommended by the viewer." Bulletin of the AMS

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  • PublisherCambridge University Press
  • Publication date2003
  • ISBN 10 0521535697
  • ISBN 13 9780521535694
  • BindingPaperback
  • LanguageEnglish
  • Edition number1
  • Number of pages428

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Hertrich-Jeromin, Udo:
Published by Cambridge University Press, 2003
ISBN 10: 0521535697 ISBN 13: 9780521535694
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Paperback. Condition: Very Good. Series: London Mathematical Society Lecture Note Series. xi 413p large paperback in very good condition, bright turquoise cover, firm binding, pages clean and neat, clear text and geometric diagrams throughout, an excellent copy Language: English Weight (g): 582. Seller Inventory # 233528

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Paperback. Condition: Like New. First Edition. Firm and square with sharp corners, just a few very minor rubs. Hence a non-text page is stamped 'damaged'. Despite such this book is actually in nearly new condition. Thus the contents are crisp, fresh and tight. And so it's now offered for sale at a very reasonable price. Seller Inventory # 116813

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Paperback. Condition: new. Paperback. This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Moebius 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. This introduction to the conformal differential geometry of surfaces and submanifolds covers those aspects of the geometry of surfaces that only refer to an angle measurement, but not to a length measurement. Different methods (models) are presented for analysis and computation. Various applications to areas of current research are discussed, including discrete net theory and certain relations between differential geometry and integrable systems theory. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Seller Inventory # 9780521535694

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