  Let M be either a simply connected pseudo-Riemannian space of constant
curvature or a rank one Riemannian symmetric space (other than the octonion
hyperbolic plane), 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)Kaehler structure on L(M).
