Curvatures of tangent hyperquadric bundles

We study geometry of tangent hyperquadric bundles over pseudo-Riemannian manifolds, which are equipped, as submanifolds of the tangent bundles, with the induced Sasaki metric. All kinds of curvatures are calculated, and geometric results concerning the Ricci curvature and the scalar curvature are proved. There exists a hyperquadric bundle whose scalar curvature is a preassigned constant.