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Lie sphere geometry : with applications to submanifolds

Author: T E Cecil
Publisher: New York : Springer, ©2008.
Series: Universitext.
Edition/Format:   eBook : Document : English : 2nd edView all editions and formats
Summary:
"This book provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean submanifold theory is established via the Legendre map, which provides a  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Cecil, T.E. (Thomas E.), 1945-
Lie sphere geometry.
New York : Springer, ©2008
(DLC) 2007936690
(OCoLC)173498965
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: T E Cecil
ISBN: 9780387746562 0387746560 9780387746555 0387746552
OCLC Number: 209985061
Description: 1 online resource (xii, 208 pages) : illustrations.
Contents: 2 Lie Sphere Geometry 9 --
2.2 Mobius Geometry of Unoriented Spheres 11 --
2.3 Lie Geometry of Oriented Spheres 14 --
2.4 Geometry of Hyperspheres in S" and H" 16 --
2.5 Oriented Contact and Parabolic Pencils of Spheres 19 --
3 Lie Sphere Transformations 25 --
3.1 The Fundamental Theorem 25 --
3.2 Generation of the Lie Sphere Group by Inversions 30 --
3.3 Geometric Description of Inversions 34 --
3.4 Laguerre Geometry 37 --
3.5 Subgeometries of Lie Sphere Geometry 46 --
4 Legendre Submanifolds 51 --
4.1 Contact Structure on [Lambda superscript 2n-1] 51 --
4.2 Definition of Legendre Submanifolds 56 --
4.3 The Legendre Map 60 --
4.4 Curvature Spheres and Parallel Submanifolds 64 --
4.5 Lie Curvatures and Isoparametric Hypersurfaces 72 --
4.6 Lie Invariance of Tautness 82 --
4.7 Isoparametric Hypersurfaces of FKM-type 95 --
4.8 Compact Proper Dupin Submanifolds 112 --
5 Dupin Submanifolds 125 --
5.1 Local Constructions 125 --
5.2 Reducible Dupin Submanifolds 127 --
5.3 Lie Sphere Geometric Criterion for Reducibility 141 --
5.4 Cyclides of Dupin 148 --
5.5 Lie Frames 159 --
5.6 Covariant Differentiation 165 --
5.7 Dupin Hypersurfaces in 4-Space 168.
Series Title: Universitext.
Responsibility: Thomas E. Cecil.

Abstract:

Thomas Cecil is a math professor with an unrivalled grasp of Lie Sphere Geometry. Here, he provides a clear and comprehensive modern treatment of the subject, as well as its applications to the study  Read more...

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Reviews from the first edition:"The book under review sets out the basic material on Lie sphere geometry in modern notation, thus making it accessible to students and researchers in differential Read more...

 
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