  We consider the orthonormal frame bundle F(M) of a Riemannian manifold M. A
construction of Sasaki defines a canonical Riemannian metric on F(M). We prove
that for two closed Riemannian n-manifolds M and N, the frame bundles F(M) and
F(N) are isometric if and only if M and N are isometric, except possibly in
dimensions 3, 4, and 8. This answers a question of Benson Farb except in
dimensions 3, 4, and 8.
