Lie sphere geometry : with applications to submanifolds
著者
書誌事項
Lie sphere geometry : with applications to submanifolds
（Universitext）
Springer-Verlag, c1992
- : New York
- : Berlin
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注記
Bibliographical references: p. [191]-200
Includes index
内容説明・目次
内容説明
This is a modern treatment of Lie's geometry of spheres, its recent applications and the study of Euclidean space. The book begins with Lie's construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres and Lie sphere transformation. The link with Euclidean submanifold theory is established via the Legendre map. This provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres. Of particular interest are isoparametric, Dupin and taut submanifolds. These have recently been classified up to Lie sphere transformation in certain special cases through the introduction of natural Lie invariants. The author provides complete proofs of these classifications and indicates directions for further research and wider application of these methods.
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