Coverart for item
The Resource Geometry of Hypersurfaces, by Thomas E. Cecil, Patrick J. Ryan, (electronic resource)

Geometry of Hypersurfaces, by Thomas E. Cecil, Patrick J. Ryan, (electronic resource)

Label
Geometry of Hypersurfaces
Title
Geometry of Hypersurfaces
Statement of responsibility
by Thomas E. Cecil, Patrick J. Ryan
Creator
Contributor
Author
Subject
Language
eng
Summary
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
Member of
http://library.link/vocab/creatorName
Cecil, Thomas E
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Ryan, Patrick J.
  • SpringerLink (Online service)
Series statement
Springer Monographs in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Topological groups
  • Lie groups
  • Differential geometry
  • Hyperbolic geometry
Label
Geometry of Hypersurfaces, by Thomas E. Cecil, Patrick J. Ryan, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-3246-7
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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
Control code
978-1-4939-3246-7
Dimensions
unknown
Edition
1st ed. 2015.
Extent
XI, 596 p. 23 illus.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493932467
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-3246-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086512140
Label
Geometry of Hypersurfaces, by Thomas E. Cecil, Patrick J. Ryan, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-1-4939-3246-7
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
Contents
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
Control code
978-1-4939-3246-7
Dimensions
unknown
Edition
1st ed. 2015.
Extent
XI, 596 p. 23 illus.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9781493932467
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-1-4939-3246-7
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086512140

Library Locations

    • Badia FiesolanaBorrow it
      Via dei Roccettini 9, San Domenico di Fiesole, 50014, IT
      43.803074 11.283055
Processing Feedback ...