On the geometry of the space of oriented lines of the hyperbolic space

SALVAI, MARCOS

GLASGOW MATHEMATICAL JOURNAL

Año: 2007 vol. 49 p. 357 - 366

0017-0895

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 ¯nd all the G-invariant pseudo-Riemannian metrics on the space Gn 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 Gn and H. Moreover, we show that G3 is KÄahler and ¯nd an orthogonal almost complex structure on G7. 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 ¯nd all the G-invariant pseudo-Riemannian metrics on the space Gn 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 Gn and H. Moreover, we show that G3 is KÄahler and ¯nd an orthogonal almost complex structure on G7.