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.
Conference chairs:
Professor Dr. Helga Baum (Berlin)
Professor Dr. Ines Kath (Greifswald)