a1 FAMAF – CIEM, Ciudad Universitaria, 5000 Córdoba, Argentina e-mail: firstname.lastname@example.org
Let H be the n-dimensional hyperbolic space of constant sectional curvature –1 and let G be the identity component of the isometry group of H. We find all the G-invariant pseudo-Riemannian metrics on the space of oriented geodesics of H (modulo orientation preserving reparametrizations). We characterize the null, time- and space-like curves, providing a relationship between the geometries of and H. Moreover, we show that is Kähler and find an orthogonal almost complex structure on .
(Received November 03 2006)
(Revised March 13 2007)
(Accepted March 19 2007)
* Partially supported by foncyt, Antorchas, ciem (conicet) and secyt (unc).