02240nam a22003498a 4500001001600000003000700016005001700023006001900040007001500059008004100074020002600115020003000141040002400171050002200195082001600217100003600233245007600269260005200345264005200397300005900449336002600508337002600534338003600560490006300596500007300659520097200732650002601704776003501730786001401765830006401779856004701843CR9780511546693UkCbUP20160624102300.0m|||||o||d||||||||cr||||||||||||090508s2003||||enk s ||1 0|eng|d a9780511546693 (ebook) z9780521535694 (paperback) aUkCbUPcUkCbUPerda00aQA609 b.H47 200300a516.3/62211 aHertrich-Jeromin, Udo,eauthor.10aIntroduction to Möbius Differential Geometry /cUdo Hertrich-Jeromin. 1aCambridge :bCambridge University Press,c2003. 1aCambridge :bCambridge University Press,c2003. a1 online resource (428 pages) :bdigital, PDF file(s). atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier0 aLondon Mathematical Society Lecture Note Series ;vno. 300 aTitle from publisher's bibliographic system (viewed on 16 Oct 2015). aThis book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed. Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers. 0aDifferential geometry08iPrint version: z9780521535694 dCambridge 0aLondon Mathematical Society Lecture Note Series ;vno. 300.40uhttp://dx.doi.org/10.1017/CBO9780511546693