Dimensional reduction of invariant linear connections and tensor fields on multidimensional space-time

Let the compact Lie group G act smoothly on the C/sup infinity/ manifold S with a single orbit type G/H, where H is a closed subgroup of G, and let N(H)/H be a Lie group [N(H) denotes the normalizer of H in G]. Assuming a given connection in the fiber bundle S → M, where M = S/G is the orbit space (to be identified with the physical space-time) and N(H)/H is the structure (gauge) group, the G-invariant tensor fields and linear connections on S are analyzed. A kind of ''dimensional reduction'' for these objects is established: every field corresponds uniquely to a field on M, and the linear connection defines uniquely a set of fields and a linear connection on M