  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.
