On the geometry of the space of oriented lines of the hyperbolic space
Differential Geometry
2007-05-23 v1
Abstract
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 OG_n 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 OG_n and H. Moreover, we show that OG_3 is K\"{a}hler and find an orthogonal almost complex structure on OG_7.
Keywords
Cite
@article{arxiv.math/0702365,
title = {On the geometry of the space of oriented lines of the hyperbolic space},
author = {Marcos Salvai},
journal= {arXiv preprint arXiv:math/0702365},
year = {2007}
}
Comments
Communicated at ICM 2006. Submitted to Glasgow Math. J. on November 3, 2006