The purpose of this article is to study the two homogeneous structures of the unit bundle UHⁿ of a real hyperbolic space, namely

and

In both the cases, we determine the G-invariant Riemannian metrics. In passing, we examine whether the geodesic flow is an isometry of  when equipped with its Levi-Civita metric.

Finally, we study the manifold of geodesics of Hⁿ seen as a homogeneous space.

hyperbolic space, isotropy representations, unit bundle

Received: April 11, 2024; Revised: June 5, 2024; Accepted: September 12, 2014; Published: December 24, 2024

How to cite this article: Alfred TOURÉ, Daniel KOAMA, Mikaïlou COMPAORÉ and Marie Françoise OUEDRAOGO, The unit bundle of a real hyperbolic space, JP Journal of Geometry and Topology 30(2) (2024), 105-117. https://doi.org/10.17654/0972415X24007

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

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