Isometry types of frame bundles
arXiv:1405.7453 · doi:10.2140/pjm.2016.285.393
Abstract
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.
Includes changes following referee's comments. 25 pages