Recent Developments in Pseudo-Riemannian Geometry [electronic resource] /
Dmitri V. Alekseevsky, Helga Baum
- Zuerich, Switzerland : European Mathematical Society Publishing House, 2008
- 1 online resource (549 pages)
- ESI Lectures in Mathematics and Physics (ESI) .
The classification problem for pseudo-Riemannian symmetric spaces / Holonomy groups of Lorentzian manifolds: classification, examples, and applications / Hypersymplectic manifolds / Anti-self-dual conformal structures in neutral signature / A neutral Kähler surface with applications in geometric optics / A primer on the (2 + 1) Einstein universe / Essential conformal structures in Riemannian and Lorentzian geometry / Conformal transformations of pseudo-Riemannian manifolds / The causal hierarchy of spacetimes / Geodesics in semi-Riemannian manifolds: geometric properties and variational tools / Lorentzian symmetric spaces in supergravity / Metric bundles of split signature and type II supergravity / Einstein metrics with 2-dimensional Killing leaves and their physical interpretation / Ines Kath, Martin Olbrich -- Anton Galaev, Thomas Leistner -- Andrew Dancer, Andrew Swann -- Maciej Dunajski, Simon West -- Brendan Guilfoyle, Wilhelm Klingenberg -- Thierry Barbot, Tomasz Kaszynski, Todd A. Drumm, William M. Goldman, Karin Melnick -- Charles Frances -- Wolfgang Kühnel, Hans-Bert Rademacher -- Ettore Minguzzi, Miguel Sánchez -- Anna Maria Candela, Miguel Sánchez -- José Miguel Figueroa-O’Farrill -- Frederik Witt -- Gaetano Vilasi.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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 art in the field as well as open problems, which can stimulate further research.
9783037195512
10.4171/051 doi
Differential & Riemannian geometry
Differential geometry
The classification problem for pseudo-Riemannian symmetric spaces / Holonomy groups of Lorentzian manifolds: classification, examples, and applications / Hypersymplectic manifolds / Anti-self-dual conformal structures in neutral signature / A neutral Kähler surface with applications in geometric optics / A primer on the (2 + 1) Einstein universe / Essential conformal structures in Riemannian and Lorentzian geometry / Conformal transformations of pseudo-Riemannian manifolds / The causal hierarchy of spacetimes / Geodesics in semi-Riemannian manifolds: geometric properties and variational tools / Lorentzian symmetric spaces in supergravity / Metric bundles of split signature and type II supergravity / Einstein metrics with 2-dimensional Killing leaves and their physical interpretation / Ines Kath, Martin Olbrich -- Anton Galaev, Thomas Leistner -- Andrew Dancer, Andrew Swann -- Maciej Dunajski, Simon West -- Brendan Guilfoyle, Wilhelm Klingenberg -- Thierry Barbot, Tomasz Kaszynski, Todd A. Drumm, William M. Goldman, Karin Melnick -- Charles Frances -- Wolfgang Kühnel, Hans-Bert Rademacher -- Ettore Minguzzi, Miguel Sánchez -- Anna Maria Candela, Miguel Sánchez -- José Miguel Figueroa-O’Farrill -- Frederik Witt -- Gaetano Vilasi.
Restricted to subscribers: http://www.ems-ph.org/ebooks.php
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 art in the field as well as open problems, which can stimulate further research.
9783037195512
10.4171/051 doi
Differential & Riemannian geometry
Differential geometry