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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Cecil, Thomas E. (Autor), Ryan, Patrick J. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: New York, NY : Springer New York : Imprint: Springer, 2015.
Edición:1st ed. 2015.
Colección:Springer Monographs in Mathematics,
Temas:
Geometry, Differential.
Topological groups.
Lie groups.
Geometry, Hyperbolic.
Differential Geometry.
Topological Groups and Lie Groups.
Hyperbolic Geometry.
Acceso en línea:Texto Completo

MARC

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245 1 0 |a Geometry of Hypersurfaces  |h [electronic resource] /  |c by Thomas E. Cecil, Patrick J. Ryan. 
250 |a 1st ed. 2015. 
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300 |a XI, 596 p. 23 illus.  |b online resource. 
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490 1 |a Springer Monographs in Mathematics,  |x 2196-9922 
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. 
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. 
650 0 |a Geometry, Differential. 
650 0 |a Topological groups. 
650 0 |a Lie groups. 
650 0 |a Geometry, Hyperbolic. 
650 1 4 |a Differential Geometry. 
650 2 4 |a Topological Groups and Lie Groups. 
650 2 4 |a Hyperbolic Geometry. 
700 1 |a Ryan, Patrick J.  |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
710 2 |a SpringerLink (Online service) 
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830 0 |a Springer Monographs in Mathematics,  |x 2196-9922 
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950 |a Mathematics and Statistics (SpringerNature-11649) 
950 |a Mathematics and Statistics (R0) (SpringerNature-43713) 

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