ESI Lectures in Mathematics and Physics 2008; 549 pp; softcover Volume: 4 ISBN10: 3037190515 ISBN13: 9783037190517 List Price: US$78 Member Price: US$62.40 Order Code: EMSESILEC/4
 This book provides an introduction to and survey of recent developments in pseudoRiemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are:  Classification of pseudoRiemannian symmetric spaces
 Holonomy groups of Lorentzian and pseudoRiemannian manifolds
 Hypersymplectic manifolds
 Antiselfdual conformal structures in neutral signature and integrable systems
 Neutral Kähler surfaces and geometric optics
 Geometry and dynamics of the Einstein universe
 Essential conformal structures and conformal transformations in pseudoRiemannian geometry
 The causal hierarchy of spacetimes
 Geodesics in pseudoRiemannian manifolds
 Lorentzian symmetric spaces in supergravity
 Generalized geometries in supergravity
 Einstein metrics with Killing leaves
The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society. Readership Graduate students and research mathematicians interested in geometry and topology. Table of Contents  I. Kath and M. Olbrich  The classification problem for pseudoRiemannian symmetric spaces
 A. Galaev and T. Leistner  Holonomy groups of Lorentzian manifolds: classification, examples, and applications
 A. Dancer and A. Swann  Hypersymplectic manifolds
 M. Dunajski and S. West  Antiselfdual conformal structures in neutral signature
 B. Guilfoyle and W. Klingenberg  A neutral Kähler surface with applications in geometric optics
 T. Barbot, V. Charette, T. Drumm, W. M. Goldman, and K. Melnick  A primer on the \((2+1)\) Einstein universe
 C. Frances  Essential conformal structures in Riemannian and Lorentzian geometry
 W. Kühnel and H.B. Rademacher  Conformal transformations of pseudoRiemannian manifolds
 E. Minguzzi and M. Sánchez  The causal hierarchy of spacetimes
 A. M. Candela and M. Sánchez  Geodesics in semiRiemannian manifolds: geometric properties and variational tools
 J. FigueroaO'Farrill  Lorentzian symmetric spaces in supergravity
 F. Witt  Metric bundles of split signature and type II supergravity
 G. Vilasi  Einstein metrics with 2dimensional Killing leaves and their physical interpretation
 List of contributors
 Index
