Hertrich-Jeromin, Udo,

Introduction to Möbius Differential Geometry / Udo Hertrich-Jeromin. - Cambridge : Cambridge University Press, 2003. - 1 online resource (428 pages) : digital, PDF file(s). - London Mathematical Society Lecture Note Series ; no. 300 . - London Mathematical Society Lecture Note Series ; no. 300. .

Title from publisher's bibliographic system (viewed on 16 Oct 2015).

This 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.

9780511546693 (ebook)

Differential geometry

QA609 / .H47 2003

The Institute of Mathematical Sciences, Chennai, India

Powered by Koha