, Volume 40, Issue 4, pp 389-409
Date: 30 Mar 2011

On the geometry of spaces of oriented geodesics

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space, and consider the space L(M) of oriented geodesics of M. The space L(M) is a smooth homogeneous manifold and in this paper we describe all invariant symplectic structures, (para)complex structures, pseudo-Riemannian metrics and (para)Kähler structure on L(M).

The first author was supported by the Leverhulme Trust, EM/9/2005/0069.