Lorentzian and conformal manifolds with special holonomy

• Applicants: Professorin Dr. Helga Baum; Privatdozent Dr. Felipe Leitner
• Subject Area: Mathematics
• Term: from 2003 to 2012
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5407150

Manifolds with special geometries can be described by their holonomy representation. The irreducible holonomy representations of Riemannian and pseudo-Riemannian manifolds are known. Geometric properties of the corresponding special geometries are currently intensively studied. In the pseudo-Riemannian case a new type of holonomy representations appears, the indecomposable, but non-irreducible ones. Each special indecomposable Lorentzian holonomy representation is non-irreducible. Contrary to the irreducible case, the indecomposable non-irreducible holonomy representations are not classified. The knowledge about the corresponding special geometric structures is rare. The aim of the project is the description of the possible holonomy representions in the Lorentzian case and the study of geometric properties of the corresponding special Lorentzian geometries including the behaviour of geometric differential equations for such manifolds.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1154: Global Differential Geometry