On the Geometry of Spaces of Oriented Geodesics

Details On the Geometry of Spaces of Oriented Geodesics On the Geometry of Spaces of Oriented Geodesics

2009-11-13

arxiv.org/abs/0911.2602v1

Mathematics

Differential Geometry

29 pages LaTEX

Scientific paper

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).

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