Fibred Riemannian spaces with contact structure (Q910731)

Let \(\pi\) : \(\tilde M\to M\) be a fibered Riemannian manifold, where M admits an (almost) Hermitian structure and each fibre admits an (almost) contact metric structure so that \(\tilde M\) admits an (almost) contact metric structure. A typical example is given by the Hopf fibration \(\pi: S^{4n+3}\to P_ n(H).\) The author studies the differential geometry of such fibered Riemannian manifolds.