Principal bundles and gauge theories in the space-time R × S3

Gauge theories on a principal fibre bundle P(M, G, π) with M = R × S3 as the base manifold and G as the structural group are considered. If G is an internal group of symmetry, we obtain the Yang-Mills gauge theories. A theory of gravitation is developed on the tangent bundle T(M). However, this is not a “pure” gauge theory. Finally, if M is endowed with a pseudo-Riemannian metric, and G is an internal group of symmetry, we obtain a unified theory of gravitation and the Yang-Mills fields.