Geometry of Hypersurfaces

This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is access...

Full description

Main Authors: Cecil, Thomas E., Ryan, Patrick J. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY Springer New York 2015, 2015
Edition:1st ed. 2015
Series:Springer Monographs in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
LEADER 03145nmm a2200361 u 4500
001 EB001086693
003 EBX01000000000000000846057
005 00000000000000.0
007 cr|||||||||||||||||||||
008 151215 ||| eng
020 |a 9781493932467 
100 1 |a Cecil, Thomas E. 
245 0 0 |a Geometry of Hypersurfaces  |h Elektronische Ressource  |c by Thomas E. Cecil, Patrick J. Ryan 
250 |a 1st ed. 2015 
260 |a New York, NY  |b Springer New York  |c 2015, 2015 
300 |a XI, 596 p. 23 illus  |b online resource 
505 0 |a Preface -- 1. Introduction -- 2. Submanifolds of Real Space Forms -- 3. Isoparametric Hypersurfaces -- 4. Submanifolds in Lie Sphere Geometry -- 5. Dupin Hypersurfaces -- 6. Real Hypersurfaces in Complex Space Forms -- 7. Complex Submanifolds of CPn and CHn -- 8. Hopf Hypersurfaces -- 9. Hypersurfaces in Quaternionic Space Forms -- Appendix A. Summary of Notation -- References -- Index 
653 |a Differential geometry 
653 |a Hyperbolic geometry 
653 |a Topological Groups, Lie Groups 
653 |a Lie groups 
653 |a Topological groups 
653 |a Differential Geometry 
653 |a Hyperbolic Geometry 
700 1 |a Ryan, Patrick J.  |e [author] 
710 2 |a SpringerLink (Online service) 
041 0 7 |a eng  |2 ISO 639-2 
989 |b Springer  |a Springer eBooks 2005- 
490 0 |a Springer Monographs in Mathematics 
856 |u https://doi.org/10.1007/978-1-4939-3246-7?nosfx=y  |x Verlag  |3 Volltext 
082 0 |a 516.36 
520 |a This exposition provides the state-of-the art on the differential geometry of hypersurfaces in real, complex, and quaternionic space forms. Special emphasis is placed on isoparametric and Dupin hypersurfaces in real space forms as well as Hopf hypersurfaces in complex space forms. The book is accessible to a reader who has completed a one-year graduate course in differential geometry. The text, including open problems and an extensive list of references, is an excellent resource for researchers in this area. Geometry of Hypersurfaces begins with the basic theory of submanifolds in real space forms. Topics include shape operators, principal curvatures and foliations, tubes and parallel hypersurfaces, curvature spheres and focal submanifolds. The focus then turns to the theory of isoparametric hypersurfaces in spheres. Important examples and classification results are given, including the construction of isoparametric hypersurfaces based on representations of Clifford algebras. An in-depth treatment of Dupin hypersurfaces follows with results that are proved in the context of Lie sphere geometry as well as those that are obtained using standard methods of submanifold theory. Next comes a thorough treatment of the theory of real hypersurfaces in complex space forms. A central focus is a complete proof of the classification of Hopf hypersurfaces with constant principal curvatures due to Kimura and Berndt. The book concludes with the basic theory of real hypersurfaces in quaternionic space forms, including statements of the major classification results and directions for further research