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OverviewThomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry. Full Product DetailsAuthor: Thomas E. CecilPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 2nd ed. 2008 Dimensions: Width: 15.50cm , Height: 1.20cm , Length: 23.50cm Weight: 0.454kg ISBN: 9780387746555ISBN 10: 0387746552 Pages: 208 Publication Date: 26 November 2007 Audience: College/higher education , Undergraduate , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsReviews from the first edition: The book under review sets out the basic material on Lie sphere geometry in modern notation, thus making it accessible to students and researchers in differential geometry...This is a carefully written, thorough, and very readable book. There is an excellent bibliography that not only provides pointers to proofs that have been omitted, but gives appropriate references for the results presented. It should be useful to all geometers working in the theory of submanifolds. - P.J. Ryan, MathSciNet The book under review is an excellent monograph about Lie sphere geometry and its recent applications to the study of submanifolds of Euclidean space...The book is written in a very clear and precise style. It contains about a hundred references, many comments of and hints to the topical literature, and can be considered as a milestone in the recent development of a classical geometry, to which the author contributed essential results. - R. Sulanke, Zentralblatt Reviews from the first edition: <p> The book under review sets out the basic material on Lie sphere geometry in modern notation, thus making it accessible to students and researchers in differential geometry.....This is a carefully written, thorough, and very readable book. There is an excellent bibliography that not only provides pointers to proofs that have been omitted, but gives appropriate references for the results presented. It should be useful to all geometers working in the theory of submanifolds. <p>- P.J. Ryan, MathSciNet <p> The book under review is an excellent monograph about Lie sphere geometry and its recent applications to the study of submanifolds of Euclidean space.....The book is written in a very clear and precise style. It contains about a hundred references, many comments of and hints to the topical literature, and can be considered as a milestone in the recent development of a classical geometry, to which the author contributed essential results. <p>- R. Sulanke, Zentralblatt Reviews from the first edition: The book under review sets out the basic material on Lie sphere geometry in modern notation, thus making it accessible to students and researchers in differential geometry.....This is a carefully written, thorough, and very readable book. There is an excellent bibliography that not only provides pointers to proofs that have been omitted, but gives appropriate references for the results presented. It should be useful to all geometers working in the theory of submanifolds. - P.J. Ryan, MathSciNet The book under review is an excellent monograph about Lie sphere geometry and its recent applications to the study of submanifolds of Euclidean space.....The book is written in a very clear and precise style. It contains about a hundred references, many comments of and hints to the topical literature, and can be considered as a milestone in the recent development of a classical geometry, to which the author contributed essential results. - R. Sulanke, Zentralblatt Author InformationProfessor Thomas E. Cecil is a professor of mathematics at Holy Cross University, where he has taught for almost thirty years. He has held visiting appointments at UC Berkeley, Brown University, and the University of Notre Dame. He has written several articles on Dupin submanifolds and hypersurfaces, and their connections to Lie sphere geometry, and co-edited two volumes on tight and taught submanifolds. Tab Content 6Author Website:Countries AvailableAll regions |
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