ENGLISH

Lie Sphere Geometry: With Applications to Submanifolds (Universitext)

By Thomas E. Cecil

Book information

Publisher
Springer
Year
2007
ISBN
0387746552, 9780387746555
Language
english
Format
PDF
Filesize
3 MB (3535369 bytes)
Pages
220\214
Time added
2024-04-15 15:38:10

Description

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.

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