WEIGHTED METRICS ON TANGENT SPHERE BUNDLES

Natural metric structures on the tangent bundle and tangent sphere bundles SrM of a Riemannian manifold M with radius function r enclose many important unsolved problems. Admitting metric connections on M with torsion, we deduce the equations of induced metric connections on those bundles. Then the equations of reducibility of TM to the almost Hermitian category. Our purpose is the study of the natural contact structure on SrM and the G2-twistor space of any oriented Riemannian 4-manifold.