Woodslane | Book - 9781470478223

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Parabolic Geometries I

Background and General Theory

ISBN-13: 9781470478223
Publisher: AMERICAN MATHEMATICAL SOCIETY
Imprint: AMERICAN MATHEMATICAL SOCIETY
By Andreas Cap, By Jan Slovak
Price: AUD $321.00
Stock: 0 in stock
Availability: This book is temporarily out of stock, order will be despatched as soon as fresh stock is received.
Local release date: 29/10/2024
Format: Paperback 628 pages Weight: 0g
Categories: Geometry [PBM]Topology [PBP]

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Table of Contents
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Google Preview: Parabolic geometries encompass a very diverse class of geometric structures, including such important examples as conformal, projective, and almost quaternionic structures, hypersurface type CR-structures 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 Bott-Borel-Weil 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.; Andreas Cap, Universitat Wien, Austria, and International Erwin Schrodinger Institute for Mathematical Physics, Wien, Austria, and Jan Slovak, Masaryk University, Brno, Czech Republic.; Background 1. Cartan geometries 2. Semisimple Lie algebras and Lie groups General theory 3. Parabolic geometries 4. A panorama of examples 5. Distinguished connections and curves Appendix A. Other prolongation procedures Appendix B. Tables; "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; Google Preview content

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Parabolic Geometries I

Background and General Theory