书目名称 | Lie Sphere Geometry | 副标题 | With Applications to | 编辑 | Thomas E. Cecil | 视频video | | 丛书名称 | Universitext | 图书封面 |  | 描述 | .Lie Sphere Geometry. provides a modern treatment of Lie‘s geometry of spheres, its recent applications and the study of Euclidean space. This 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. | 出版日期 | Book 19921st edition | 关键词 | Invariant; Lie; Natural; character; classification; construction; curvature; form; framework; geometry; manifo | 版次 | 1 | doi | https://doi.org/10.1007/978-1-4757-4096-7 | isbn_ebook | 978-1-4757-4096-7Series ISSN 0172-5939 Series E-ISSN 2191-6675 | issn_series | 0172-5939 | copyright | Springer Science+Business Media New York 1992 |
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