Fields and connections in a fiber bundle over spacetime arising from the reduction of the multidimensional linear connection

Abstract

We consider the invariant linear connections in a multidimensional universe where a compact connected Lie groupG acts with a single orbit typeG/H. It is shown that every such connection reduces to a principal connection in a dimensionally-reduced fiber bundle over the four-dimensional spacetimeM and to a set of fields onM with a gauge group isomorphic toN/H × GL(4,R), whereN is the normalizer inG of the closed subgroupH.