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008 150903s2008 xxu| o |||| 0|eng d
020 _a9780387746562
_99780387746562
024 7 _a10.1007/9780387746562
_2doi
035 _avtls000332523
039 9 _a201509030230
_bVLOAD
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_dVLOAD
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040 _aMX-SnUAN
_bspa
_cMX-SnUAN
_erda
050 4 _aQA641-670
100 1 _aCecil, Thomas E.
_eautor
_9304159
245 1 0 _aLie Sphere Geometry :
_bWith Applications to Submanifolds /
_cby Thomas E. Cecil.
264 1 _aNew York, NY :
_bSpringer New York,
_c2008.
300 _brecurso en línea.
336 _atexto
_btxt
_2rdacontent
337 _acomputadora
_bc
_2rdamedia
338 _arecurso en línea
_bcr
_2rdacarrier
347 _aarchivo de texto
_bPDF
_2rda
500 _aSpringer eBooks
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
590 _aPara consulta fuera de la UANL se requiere clave de acceso remoto.
710 2 _aSpringerLink (Servicio en línea)
_9299170
776 0 8 _iEdición impresa:
_z9780387746555
856 4 0 _uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-0-387-74656-2
_zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999 _c279690
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