The Resource Lie Sphere Geometry : With Applications to Submanifolds, by Thomas E. Cecil, (electronic resource)

Lie Sphere Geometry : With Applications to Submanifolds, by Thomas E. Cecil, (electronic resource)

Label
Lie Sphere Geometry : With Applications to Submanifolds
Title
Lie Sphere Geometry
Title remainder
With Applications to Submanifolds
Statement of responsibility
by Thomas E. Cecil
Creator
Author
Author
Subject
Language
  • eng
  • eng
Summary
This book provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean submanifold theory is established via the Legendre map, which provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres. This new edition contains revised sections on taut submanifolds, compact proper Dupin submanifolds, reducible Dupin submanifolds, and the cyclides of Dupin. Completely new material on isoparametric hypersurfaces in spheres and Dupin hypersurfaces with three and four principal curvatures is also included. The author surveys the known results in these fields and indicates directions for further research and wider application of the methods of Lie sphere geometry. Further key features of Lie Sphere Geometry 2/e: - Provides the reader with all the necessary background to reach the frontiers of research in this area - Fills a gap in the literature; no other thorough examination of Lie sphere geometry and its applications to submanifold theory - Complete treatment of the cyclides of Dupin, including 11 computer-generated illustrations - Rigorous exposition driven by motivation and ample examples. Reviews from the first edition: "The book under review sets out the basic material on Lie sphere geometry in modern notation, thus making it accessible to students and researchers in differential geometry.....This is a carefully written, thorough, and very readable book. There is an excellent bibliography that not only provides pointers to proofs that have been omitted, but gives appropriate references for the results presented. It should be useful to all geometers working in the theory of submanifolds." - P.J. Ryan, MathSciNet "The book under review is an excellent monograph about Lie sphere geometry and its recent applications to the study of submanifolds of Euclidean space.....The book is written in a very clear and precise style. It contains about a hundred references, many comments of and hints to the topical literature, and can be considered as a milestone in the recent development of a classical geometry, to which the author contributed essential results." - R. Sulanke, Zentralblatt
Member of
http://library.link/vocab/creatorName
Cecil, Thomas E
Dewey number
516.36
http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
JZM-oWlQOO4
Language note
English
LC call number
QA641-670
Literary form
non fiction
Nature of contents
dictionaries
Series statement
Universitext,
http://library.link/vocab/subjectName
  • Global differential geometry
  • Geometry, algebraic
  • Cell aggregation
  • Differential Geometry
  • Algebraic Geometry
  • Manifolds and Cell Complexes (incl. Diff.Topology)
Label
Lie Sphere Geometry : With Applications to Submanifolds, by Thomas E. Cecil, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (P. [191]-199) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Lie Sphere Geometry -- Lie Sphere Transformations -- Legendre Submanifolds -- Dupin Submanifolds
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (213 p.)
Form of item
online
Isbn
9780387746562
Media category
computer
Media type code
c
Other control number
10.1007/978-0-387-74656-2
Specific material designation
remote
System control number
  • (CKB)1000000000492029
  • (EBL)3062966
  • (SSID)ssj0000318661
  • (PQKBManifestationID)11247241
  • (PQKBTitleCode)TC0000318661
  • (PQKBWorkID)10311622
  • (PQKB)10578309
  • (DE-He213)978-0-387-74656-2
  • (MiAaPQ)EBC3062966
  • (EXLCZ)991000000000492029
Label
Lie Sphere Geometry : With Applications to Submanifolds, by Thomas E. Cecil, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (P. [191]-199) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
Lie Sphere Geometry -- Lie Sphere Transformations -- Legendre Submanifolds -- Dupin Submanifolds
Dimensions
unknown
Edition
2nd ed.
Extent
1 online resource (213 p.)
Form of item
online
Isbn
9780387746562
Media category
computer
Media type code
c
Other control number
10.1007/978-0-387-74656-2
Specific material designation
remote
System control number
  • (CKB)1000000000492029
  • (EBL)3062966
  • (SSID)ssj0000318661
  • (PQKBManifestationID)11247241
  • (PQKBTitleCode)TC0000318661
  • (PQKBWorkID)10311622
  • (PQKB)10578309
  • (DE-He213)978-0-387-74656-2
  • (MiAaPQ)EBC3062966
  • (EXLCZ)991000000000492029

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