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Introduction to Möbius Differential Geometryby Udo Hertrich-Jeromin; J. W. S. Cassels
Cambridge University Press 2003; US$ 58.00An introduction to the conformal differential geometry of surfaces and submanifolds. The book discusses those aspects of the geometry of surfaces that only refer to an angle measurement but not to a length measurement. The book presents different methods (models) for thinking about geometry and performing computations. more...
Recent Progress In Conformal Geometryby Abbas Bahri; Yongzhong Xu
World Scientific 2007; US$ 140.40This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular. New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This family of problems, thought to be out of reach a few years ago, becomes a family of problems which can be studied: the book lays the foundation for a program of research in this direction. In contact form geometry, a cousin of symplectic geometry, the authors prove a fundamental result of compactness in a variational problem on Legrendrian curves, which allows one to define a homology associated to a contact structure and a vector field of its kernel on a three-dimensional manifold.... more...
The Ambient Metric (AM-178)by Charles Fefferman; C. Robin Graham
Princeton University Press 2011; US$ 80.00This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n + 2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n + 1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics. The existence and uniqueness of the ambient metric at the formal power series level is treated in detail. This includes the derivation of the ambient obstruction tensor and an explicit analysis of the special cases of conformally flat and conformally Einstein spaces. Poincaré metrics... more...
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