1. Study of homogeneous models in string theory and their field equations in the bosonic as well as in the fermionic sector.

2. Investigations of the holonomy group, curvature and parallel objects of affine connections with torsion, in particular on homogeneous reductive spaces.

3. Application of Kostant's connection and the Dirac operator induced by it to realization problems for representations of semisimple Lie groups; study of the spectral properties of invariant differential operators appearing in this context.