Generalized Cheeger-Gromoll Metrics and the Hopf map
Differential Geometry
2010-02-10 v2
Abstract
We show, using two different approaches, that there exists a family of Riemannian metrics on the tangent bundle of a two-sphere, which induces metrics of constant curvature on its unit tangent bundle. In other words, given such a metric on the tangent bundle of a two-sphere, the Hopf map is identified with a Riemannian submersion from the universal covering space of the unit tangent bundle onto the two-sphere. A hyperbolic counterpart dealing with the tangent bundle of a hyperbolic plane is also presented.
Cite
@article{arxiv.0808.1644,
title = {Generalized Cheeger-Gromoll Metrics and the Hopf map},
author = {M. Benyounes and E. Loubeau and S. Nishikawa},
journal= {arXiv preprint arXiv:0808.1644},
year = {2010}
}
Comments
17 pages, Dedicated to Professor Udo Simon on his seventieth birthday