Kaluza–Klein theories on bundles with homogeneous fibers. I

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Abstract
We analyze some geometric aspects of Kaluza–Klein theories under the assumption that the (4+d)-dimensional space is a bundle over space–time M with fiber G/H. We formulate the most general metric in the bundle which leads, upon dimensional reduction of the Ricci scalar, to a G-gauge invariant Lagrangian. We find that the treatment of Brans–Dicke-like scalars given by some authors is inconsistent with the bundle-theoretic interpretation.