
Preface  Preview Material  Table of Contents  Supplementary Material 
Mathematical Surveys and Monographs 2009; 628 pp; hardcover Volume: 154 ISBN10: 0821826816 ISBN13: 9780821826812 List Price: US$120 Member Price: US$96 Order Code: SURV/154 See also: An Introduction to CR Structures  Howard Jacobowitz Conformal, Riemannian and Lagrangian Geometry: The 2000 Barrett Lectures  SunYung A Chang, Paul C Yang, Karsten Grove, Jon G Wolfson and edited by Alexandre Freire  Parabolic geometries encompass a very diverse class of geometric structures, including such important examples as conformal, projective, and almost quaternionic structures, hypersurface type CRstructures and various types of generic distributions. The characteristic feature of parabolic geometries is an equivalent description by a Cartan geometry modeled on a generalized flag manifold (the quotient of a semisimple Lie group by a parabolic subgroup). Background on differential geometry, with a view towards Cartan connections, and on semisimple Lie algebras and their representations, which play a crucial role in the theory, is collected in two introductory chapters. The main part discusses the equivalence between Cartan connections and underlying structures, including a complete proof of Kostant's version of the BottBorelWeil theorem, which is used as an important tool. For many examples, the complete description of the geometry and its basic invariants is worked out in detail. The constructions of correspondence spaces and twistor spaces and analogs of the Fefferman construction are presented both in general and in several examples. The last chapter studies Weyl structures, which provide classes of distinguished connections as well as an equivalent description of the Cartan connection in terms of data associated to the underlying geometry. Several applications are discussed throughout the text. Readership Graduate students and research mathematicians interested in parabolic geometry, conformal geometry, almost quaternionic structures, and CRstructures. Reviews "An excellent book. Serving both as a timely introduction to parabolic geometry and as a general introductory work for Lie groups and Cartan geometries. ... This review cannot do justice to the power and generality of parabolic geometry theory, but this book certainly does."  Mathematical Reviews 


AMS Home 
Comments: webmaster@ams.org © Copyright 2014, American Mathematical Society Privacy Statement 