Invariant Connections with Torsion on Group Manifolds and Their Application in Kaluza-Klein Theories

Invariant connections with torsion on simple group manifolds $S$ are studied and an explicit formula describing them is presented. This result is used for the dimensional reduction in a theory of multidimensional gravity with curvature squared terms on $M^4\times S$. We calculate the potential of scalar fields, emerging from extra components of the metric and torsion, and analyze the role of the torsion for the stability of spontaneous compactification.