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Recent Developments in Pseudo-Riemannian Geometry
Edited by: Dmitri V. Alekseevsky, Edinburgh University, Scotland, and Helga Baum, Humboldt-Universität, Berlin, Germany
A publication of the European Mathematical Society.
ESI Lectures in Mathematics and Physics
2008; 549 pp; softcover
Volume: 4
ISBN-10: 3-03719-051-5
ISBN-13: 978-3-03719-051-7
List Price: US$78
Member Price: US$62.40
Order Code: EMSESILEC/4
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This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are:

  • Classification of pseudo-Riemannian symmetric spaces
  • Holonomy groups of Lorentzian and pseudo-Riemannian manifolds
  • Hypersymplectic manifolds
  • Anti-self-dual 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 pseudo-Riemannian geometry
  • The causal hierarchy of spacetimes
  • Geodesics in pseudo-Riemannian 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.


Graduate students and research mathematicians interested in geometry and topology.

Table of Contents

  • I. Kath and M. Olbrich -- The classification problem for pseudo-Riemannian 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 -- Anti-self-dual 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 pseudo-Riemannian manifolds
  • E. Minguzzi and M. Sánchez -- The causal hierarchy of spacetimes
  • A. M. Candela and M. Sánchez -- Geodesics in semi-Riemannian manifolds: geometric properties and variational tools
  • J. Figueroa-O'Farrill -- Lorentzian symmetric spaces in supergravity
  • F. Witt -- Metric bundles of split signature and type II supergravity
  • G. Vilasi -- Einstein metrics with 2-dimensional Killing leaves and their physical interpretation
  • List of contributors
  • Index
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