Pseudo-Riemannian metrics on manifolds are a generalization of Riemannian metrics to the indefinite case. The most popular examples are metrics with Lorentzian signature, which occur as models for space-times in general relativity. Whereas the Riemannian situation is well studied and a rather satisfactory theory including special geometric structures or manifolds with special curvature properties was established, similar results for pseudo-Riemannian manifolds are rare and even many basic problems are still unsolved. However, in recent years enormous progress was made in this field. A strong motivation for this development comes from theoretical physics, in particular from supergravity and string theory, where a deeper understanding of geometric structures of higher dimensional manifolds with indefinite metrics of different signature is needed.
 
The Summer Academy on Lorentzian Geometry will deal with the geometry of pseudo-Riemannian manifolds with special holonomy, the classification of pseudo-Riemannian homogeneous and symmetric spaces, the transformation groups in pseudo-Riemannian geometry, the  classification of pseudo-Riemannian manifolds with special curvature properties, its applications to general relativity, to supergravity and string theory, and operators of Laplacian and Dirac type on Lorentzian manifolds.
 
 
July 20-22, 2009
 
Programme of the Summer School
^{(PDF file)} 
 
Abstracts of the talks
^{(PDF file)} 
 
List of registered participants
^{(PDF file; updated July 14, 2009)} 
 
Conference chairs:
Professor Dr. Helga Baum (Berlin)
Professor Dr. Ines Kath (Greifswald)
 
Information:
tagungsbuero(at)wiko-greifswald.de
 
 
Programme:
 
Monday, July 20, 2009
9:00    Andrzej Derdzinski

Geometric conditions leading to Patterson-Walker extension metrics

10:00  Karin Melnick

Nilpotent groups of conformal flows on pseudo-Riemannian manifold

11:30  Carlos Olmos

Submanifold geometry and Berger-type theorems

15:00  Dmitri Alekseevsky

Pseudo-Riemannian manifolds with many Killing spinors

16:30  Jürgen Berndt

Cohomogeneity one actions on symmetric spaces of noncompact type

17:30  Martin Olbrich

Non-semisimple variants of classical pseudo-Riemannian symmetric spaces

 
Tuesday, July 21, 2009
9:00   Christian Bär

Dirac type operators on Lorentzian manifolds

10:00  Lars Andersson

Hidden symmetries and the wave equation on Kerr

11:30  Marie-Amélie Lawn

Pluriminimal immersions of pseudo-Riemannian manifolds into indefinite euclidean spaces

Jürgen Tolksdorf

Real bi-graded Clifford modules, the Majorana equation and the
Standard Model Action

15:00  Alan Rendall

The Einstein-Maxwell equations and complex hyperbolic plane

16:30  Piotr T. Chruściel

On higher dimensional black holes

17:30  Felix Finster

Causal variational principles in discrete and continuum space-times

 
Wednesday, July 22, 2009
9:00    Vicente Cortés

Half-flat structures and special holonomy

10:00  Thomas Leistner

Conformal pp-waves and their ambient metrics

11:30  Matthias Plaue

Geometrical Aspects of Time Machines
Kishore Marathe
Generalized gravitational instantons
Katja Sagerschnig
Conformal structures associated to generic rank 2 distributions in dimension 5

15:00  Marc Nardmann

Some global Ricci and scalar curvature problems in Lorentzian geometry

16:30  Vladimir Matveev

Projective transformation of pseudo-Riemannian manifolds: rigidity of Einstein manifolds and Lichnerowich conjecture

17:30  Alexey Bolsinov

Projectively equivalent pseudo-Riemannian metrics and integrable so(p,q)-tops