Isometry types of frame bundles
Differential Geometry
2016-11-30 v2
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.
Keywords
Cite
@article{arxiv.1405.7453,
title = {Isometry types of frame bundles},
author = {Wouter van Limbeek},
journal= {arXiv preprint arXiv:1405.7453},
year = {2016}
}
Comments
Includes changes following referee's comments. 25 pages