.

0 (hodnocen0 x )

BK

Providence : American Mathematical Society, c2009

x, 628 s. ; 27 cm

ISBN 978-0-8218-2681-2 (váz.)

Mathematical surveys and monographs ; vol. 154

Obsahuje bibliografii na s. 617-622 a rejstřík

000239014

Preface // Part 1. // Background // Contents // • • // Vil // Chapter 1. Cartan geometries 3 // 1.1. Prologue - a few examples of homogeneous spaces 4 // 1.2. Some background from differential geometry 15 // 1.3. A survey on connections 35 // 1.4. Geometry of homogeneous spaces 49 // 1.5. Cartan connections 70 // 1.6. Conformal Riemannian structures 112 // Chapter 2. Semisimple Lie algebras and Lie groups 141 // 2.1. Basic structure theory of Lie algebras 141 // 2.2. Complex semisimple Lie algebras and their representations 160 // 2.3. Real semisimple Lie algebras and their representations 199 // Part 2. General theory 231 // Chapter 3. Parabolic geometries 233 // 3.1. Underlying structures and normalization 234 // 3.2. Structure theory and classification 290 // 3.3. Kost ant’s version of the Bott-Borel-Weil theorem 339 // Historical remarks and references for Chapter 3 360 // Chapter 4. A panorama of examples 363 // 4.1. Structures corresponding to 1-gradings 363 // 4.2. Parabolic contact structures 402 // 4.3. Examples of general parabolic geometries 426 // 4.4. Correspondence spaces and twistor spaces 455 // 4.5. Analogs of the Fefferman construction 478 // Chapter 5. Distinguished connections and curves 497 // 5.1. Weyl structures and scales 498 // 5.2. Characterization of Weyl structures 517 // 5.3. Canonical curves 558 // vi // CONTENTS // Appendix A. // Appendix B. // Bibliography // Other prolongation procedures // Tables // 599 // 607 // 617 // Index

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