Canonical connections on Riemannian symmetric spaces and solutions to the Einstein-Yang-Mills equations

It is shown that for any principal bundle over a Riemannian symmetric space G /G₀ which admits G as automorphism group, the canonical G-invariant connection satisfies the source free gauge field equations. Extending this to product manifolds V × G /G₀ and assuming the metric and gauge fields decompose in a natural way, this result is still valid and the Einstein equations with gauge fields as source may also be satisfied. For G /G₀, this is so automatically, but with a cosmological term present. For dimV = 1 or 2, solutions are found, yielding metrics of the Robertson-Walker and Reissner-Nordstrom type.