On the geometry of orthonormal frame bundles II

We study the geometry of orthonormal frame bundles OM over Riemannian manifolds ( M, g). The former are equipped with some modifications (g) over tilde (c) of the Sasaki-Mok metric (g) over tilde depending on one real parameter c not equal 0. The metrics (g) over tilde (c) are " strongly invariant" in some special sense. In particular, we consider the case when ( M, g) is a space of constant sectional curvature K. Then, for dim M > 2, we find always, among the metrics (g) over tilde (c), two strongly invariant Einstein metrics on OM which are Riemannian for K > 0 and pseudo-Riemannian for K < 0. At least one of them is not locally symmetric. We also find, for dim M >= 2, two invariant metrics with vanishing scalar curvature.