This book provides a modern treatment of Lie's geometry of spheres, its applications and the study of Euclidean space. It 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. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, Lie frames and frame reductions. Completely new material on isoparametric hyperspaces in spheres, Dupin hyperspaces with three and four principle curvatures is also included.
| ISBN: | 9780387746555 |
| Publication date: | 26th November 2007 |
| Author: | T E Cecil |
| Publisher: | Springer an imprint of Springer New York |
| Format: | Paperback |
| Pagination: | 208 pages |
| Series: | Universitext |
| Genres: |
Differential and Riemannian geometry Algebraic geometry Topology |
This book provides a modern treatment of Lie's geometry of spheres, its applications and the study of Euclidean space. It 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. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, Lie frames and frame reductions. Completely new material on isoparametric hyperspaces in spheres, Dupin hyperspaces with three and four principle curvatures is also included.
Lie Sphere Geometry features in the following genres: Differential and Riemannian geometry, Algebraic geometry, Topology
Lie Sphere Geometry is available in Paperback
Lie Sphere Geometry was written by T E Cecil and published by Springer an imprint of Springer New York
Lie Sphere Geometry has 208 pages
Yes it is part of Universitext series
£53.99