Lie sphere geometry : with applications to submanifolds
著者
書誌事項
Lie sphere geometry : with applications to submanifolds
（Universitext）
Springer, c2008
2nd ed
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注記
Includes bibliographical references (p. [191]-199) and index
内容説明・目次
内容説明
Thomas 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.
目次
Lie Sphere Geometry.- Lie Sphere Transformations.- Legendre Submanifolds.- Dupin Submanifolds.
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