On Riemannian geometry of orthonormal frame bundles

Abstract

O. Kowalski and the present author have studied systematically Riemannian geometry of the metric on the orthonormal frame bundle induced by the Sasaki-Mok metric on the linear frame bundle. We have also studied more general metrics which rescale the horizontal part by a nonzero constant. In particular, we have obtained nonstandard Einstein metrics and also metrics with zero scalar curvature on the orthonormal frame bundles over any space of constant sectional curvature. In the present paper, we shall survey our results without detailed proofs.