Universitext

Lie Sphere Geometry

With Applications to Submanifolds

Authors: Cecil, Thomas E.

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About this Textbook

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)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4757-4096-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Lie Sphere Geometry
Book Subtitle
With Applications to Submanifolds
Authors
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