Geometry of Hypersurfaces

Nonfiction, Science & Nature, Mathematics, Group Theory, Geometry
Cover of the book Geometry of Hypersurfaces by Patrick J. Ryan, Thomas E. Cecil, Springer New York
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Patrick J. Ryan, Thomas E. Cecil ISBN: 9781493932467
Publisher: Springer New York Publication: October 30, 2015
Imprint: Springer Language: English
Author: Patrick J. Ryan, Thomas E. Cecil
ISBN: 9781493932467
Publisher: Springer New York
Publication: October 30, 2015
Imprint: Springer
Language: English

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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

More books from Springer New York

Cover of the book Polymer Macro- and Micro-Gel Beads: Fundamentals and Applications by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Lecture Notes on the General Theory of Relativity by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Pediatric Neuro-Ophthalmology by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Neural Computation, Neural Devices, and Neural Prosthesis by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Opioids, Bulimia, and Alcohol Abuse & Alcoholism by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Cytoskeleton of the Nervous System by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Plant Mitochondria by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Measuring Technology and Mechatronics Automation in Electrical Engineering by Patrick J. Ryan, Thomas E. Cecil
Cover of the book The Painted Stork by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Probability-2 by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Prokaryotic Antimicrobial Peptides by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Neuroanatomy by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Mindfulness and Acceptance in Couple and Family Therapy by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Guide to Psychological Assessment with Asians by Patrick J. Ryan, Thomas E. Cecil
Cover of the book Proteases in Health and Disease by Patrick J. Ryan, Thomas E. Cecil
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy