Riemannian geometry, fiber bundles, Kaluza-Klein theories and all that

This book discusses the geometrical aspects of Kaluza-Klein theories. The ten chapters cover topics from the differential and Riemannian manifolds to the reduction of Einstein-Yang-Mills action. It would definitely prove interesting reading to physicists and mathematicians, theoretical and experimental. Contents: Generalities; Riemannian Geometry of Lie Groups; Riemannian Geometry of Homogeneous Spaces; Riemannian Geometry of a (Right) Principal Bundle; Riemannian Geometry of a Bundle with Fibers and a Given Action of a Lie Group G; Geometry of Matter Fields; Harmonic Analysis and Dimensional Reduction; Dimensional Reduction of the Orthogonal Bundle and of the Spin Bundles; G-Invariance of Einstein-Yang-Mills Systems; Action of a Bundle of Groups