000 04061nam a22004695i 4500
001 978-0-387-74656-2
003 DE-He213
005 20161121231208.0
007 cr nn 008mamaa
008 100301s2008 xxu| s |||| 0|eng d
020 _a9780387746562
_9978-0-387-74656-2
024 7 _a10.1007/978-0-387-74656-2
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36
_223
100 1 _aCecil, Thomas E.
_eauthor.
245 1 0 _aLie Sphere Geometry
_h[electronic resource] :
_bWith Applications to Submanifolds /
_cby Thomas E. Cecil.
264 1 _aNew York, NY :
_bSpringer New York,
_c2008.
300 _aXII, 208 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aLie Sphere Geometry -- Lie Sphere Transformations -- Legendre Submanifolds -- Dupin Submanifolds.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aAlgebraic geometry.
650 0 _aDifferential geometry.
650 0 _aManifolds (Mathematics).
650 0 _aComplex manifolds.
650 1 4 _aMathematics.
650 2 4 _aDifferential Geometry.
650 2 4 _aAlgebraic Geometry.
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780387746555
856 4 0 _uhttp://dx.doi.org/10.1007/978-0-387-74656-2
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c509955
_d509955