Geometry of Hypersurfaces

Thomas E. Cecil, Patrick J. Ryan

$278.95 $222.98

Paperback

Not in-store but you can order this
How long will it take?

Availability Information

We source books from suppliers in Australia and overseas. For books we don't currently have in stock, the time it takes to get them from our suppliers can vary widely - from a few days to a few months - so we check each book with each supplier to determine the expected time it will take to be supplied to us.

We then advise you accordingly. If the time taken to get any book is too long for you, you can let us know and we will cancel or adjust your order, and refund as required.

To find out the anticipated arrival time for specific items prior to ordering, please contact us by phone or email:

Phone +61 2 9264 3111, or 1800 4 BOOKS (1800 4 26657) if outside Sydney:
option 1 Abbey's Bookshop (Crime, History, Science, Kids & more) • info@abbeys.com.au
option 2 Language Book Centre (ESL & Foreign Languages) • language@abbeys.com.au
option 3 Galaxy Bookshop (Sci-fi, Fantasy, Romance, Graphic Novels) • sf@galaxybooks.com.au

QTY:

English

Springer-Verlag New York Inc.
23 August 2016

Groups & group theory; Non-Euclidean geometry; Differential & Riemannian geometry

Series: Springer Monographs in Mathematics

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.

By: Thomas E. Cecil, Patrick J. Ryan
Imprint: Springer-Verlag New York Inc.
Country of Publication: United States
Edition: Softcover reprint of the original 1st ed. 2015
Dimensions: Height: 235mm, Width: 155mm,
Weight: 9.066kg
ISBN: 9781493945078
ISBN 10: 1493945076
Series: Springer Monographs in Mathematics
Pages: 596
Publication Date: 23 August 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Thomas E. Cecil is professor of mathematics at the College of Holy Cross in Worcester, MA, USA. His primary research interests are in differential geometry, in particular, submanifolds. Patrick J. Ryan is Emeritus professor of mathematical sciences at McMaster University in Hamilton, Ontario, Canada. His primary research interests are in Geometry, in particular, the characterization and classification of hypersurfaces in real and complex space forms.

Reviews for Geometry of Hypersurfaces

This 600-page book is the result of the authors' efforts to provide a detailed presentation of the present day differential geometry of hypersurfaces in real, complex, and quaternionic space forms. ... A summary of the frequently used notations and an index of notions are included. The book is an essential contribution to the progress of the theory of hypersurfaces. (Radu Miron, zbMATH 1331.53001, 2016)