04077nam a22004455i 4500001001800000003000900018005001700027007001500044008004100059020001800100020001900118024003500137040000900172082001500181100003000196245010900226264004600335300002100381336002600402337002600428338003900454347002400493505010200517520245500619650001703074650002503091650003403116650003503150650001703185650002703202650002403229650005603253710003403309773002003343776003603363856010303399942001203502999001703514952010003531978-0-387-74656-2DE-He21320260521091949.0cr nn 008mamaa100301s2008    xxu|    s    |||| 0|eng d  a9780387746562  a997803877465627 a10.1007/978-0-387-74656-22doi  cCICY04a516.362231 aCecil, Thomas E.eauthor.10aLie Sphere Geometryh[recurso electrónico] :bWith Applications to Submanifolds /cby Thomas E. Cecil. 1aNew York, NY :bSpringer New York,c2008.  bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  arecurso en líneabcr2rdacarrier  atext filebPDF2rda0 aLie Sphere Geometry -- Lie Sphere Transformations -- Legendre Submanifolds -- Dupin Submanifolds.  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 0aMATHEMATICS. 0aGEOMETRY, ALGEBRAIC. 0aGLOBAL DIFFERENTIAL GEOMETRY. 0aCELL AGGREGATIONxMATHEMATICS.14aMATHEMATICS.24aDIFFERENTIAL GEOMETRY.24aALGEBRAIC GEOMETRY.24aMANIFOLDS AND CELL COMPLEXES (INCL. DIFF.TOPOLOGY).2 aSpringerLink (Online service)0 tSpringer eBooks08iPrinted edition:z978038774655540uhttp://dx.doi.org/10.1007/978-0-387-74656-2zVer el texto completo en las instalaciones del CICY  2ddccER  c34553d34553  00102ddc40708LEaCICYbCICYcELd2025-07-10l0o516.36r2025-07-10 08:40:20w2025-07-10yER