Sfb 288 Differential Geometry and Quantum Physics

Spinor field equations and Lorentzian geometry

Leader(s):

Prof. Dr. sc. Helga Baum

The main objective of the project Spinor field equations and Lorentzian geometry is to study the conditions to the existence of solutions of spinor field equations on manifolds with indefinite metric. The relation of these conditions to properties of the underlying geometry and in particular all effects caused by indecomposable and non-irreducible holonomy representations (which do not occur in the definite case) are of interest.
The project contains the following special research areas:

1. The classification of special geometric structures that admit solutions to spinor field equations that are relevant in geometry (twistor-type equations) and recently in supergravitation- and superstring theory.
2. The investigation of indefinite manifolds with indecomposable and non-irreducible holonomy representation and large isometry group (in particular symmetric and homogeneous spaces) .
3. The investigation of possible indecomposable and non-irreducible holonomy representations and their local or global realisation.
4. The relation between conditions to the existence of solutions to the Dirac equation on Lorentzian manifolds and properties of lightlike geodesics such as completeness and dynamics.