Introduction to Möbius Differential Geometry

ISBN-13: 9780521535694 / Angielski / Miękka / 2003 / 428 str.

Udo Hertrich-Jeromin

Opis

This introduction to the conformal differential geometry of surfaces and submanifolds covers those aspects of the geometry of surfaces that only refer to an angle measurement, but not to a length measurement. Different methods (models) are presented for analysis and computation. Various applications to areas of current research are discussed, including discrete net theory and certain relations between differential geometry and integrable systems theory.

Recenzje

'This book is a work of scholarship, communicating the author's enthusiasm for Möbius geometry very clearly. The book will serve as an introduction to Möbius geometry to newcomers, and as a very useful reference for research workers in the field.' Tom Willmore, University of Durham

Spis treści

Introduction; 0. Preliminaries: the Riemannian point of view; 1. The projective model; 2. Application: conformally flat hypersurfaces; 3. Application: isothermic and Willmore surfaces; 4. A quaternionic model; 5. Application: smooth and discrete isothermic surfaces; 6. A Clifford algebra model; 7. A Clifford algebra model; Vahlen matrices; 8. Applications: orthogonal systems, isothermic surfaces; Conclusion.