Buy this book
- About this book
-
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.
- Table of contents (5 chapters)
-
-
Introduction
Pages 1-7
-
Lie Sphere Geometry
Pages 8-28
-
Lie Sphere Transformations
Pages 29-64
-
Legendre Submanifolds
Pages 65-128
-
Dupin Submanifolds
Pages 129-190
-
Table of contents (5 chapters)
Recommended for you
Bibliographic Information
- Bibliographic Information
-
- Book Title
- Lie Sphere Geometry
- Book Subtitle
- With Applications to Submanifolds
- Authors
-
- Thomas E. Cecil
- Series Title
- Universitext
- Copyright
- 1992
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer Science+Business Media New York
- eBook ISBN
- 978-1-4757-4096-7
- DOI
- 10.1007/978-1-4757-4096-7
- Series ISSN
- 0172-5939
- Edition Number
- 1
- Number of Pages
- XII, 209
- Topics
