| 书目名称 | Geometry of Hypersurfaces |
| 编辑 | Thomas E. Cecil,Patrick J. Ryan |
| 视频video | |
| 概述 | Presents thorough treatment of hypersurfaces in real, complex, and quaternionic space forms with connections to symmetric spaces, homogeneous spaces, and Riemannian geometry.Treats Dupin hypersurfaces |
| 丛书名称 | Springer Monographs in Mathematics |
| 图书封面 |  |
| 描述 | .This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area..Geometry of Hypersurfaces. begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hypersurfaces follows with results that are proved in the context of Lie sphere geometry as well as those that are obtained using standard methods of submanifold theory. Next c |
| 出版日期 | Book 2015 |
| 关键词 | Dupin hypersurfaces; Hopf hypersurfaces; Lie sphere geometry; differential geometry submanifolds; geomet |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4939-3246-7 |
| isbn_softcover | 978-1-4939-4507-8 |
| isbn_ebook | 978-1-4939-3246-7Series ISSN 1439-7382 Series E-ISSN 2196-9922 |
| issn_series | 1439-7382 |
| copyright | Thomas E. Cecil and Patrick J. Ryan 2015 |
发表于 2025-3-21 17:44:27
