Generalized Cheeger-Gromoll Metrics and the Hopf map

Details Generalized Cheeger-Gromoll Metrics and the Hopf map Generalized Cheeger-Gromoll Metrics and the Hopf map

2008-08-12

arxiv.org/abs/0808.1644v2

Mathematics

Differential Geometry

17 pages, Dedicated to Professor Udo Simon on his seventieth birthday

Scientific paper

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.

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