Introduction to M}}bius Differential Geometry [Paperback]

This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere.An introduction, at a basic level, to the conformal differential geometry of surfaces and submanifolds is given. That is, the book discusses those aspects of the geometry of surfaces that does only refer to an angle measurement but not to a length measurement. Different methods (models) to think about their geometry as well as to do computations are presented. Various applications to areas of current research interest are discussed, including discrete net theory and certain relations between differential geometry and integrable systems theory.An introduction, at a basic level, to the conformal differential geometry of surfaces and submanifolds is given. That is, the book discusses those aspects of the geometry of surfaces that does only refer to an angle measurement but not to a length measurement. Different methods (models) to think about their geometry as well as to do computations are presented. Various applications to areas of current research interest are discussed, including discrete net theory and certain relations between differential geometry and integrable systems theory.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.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 matriceslS¶