On the geometry of spaces of oriented geodesics
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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).
KeywordsSpace of geodesics Homogeneous manifolds Pseudo-Riemannian metrics Symplectic structures Kähler structures
Mathematics Subject Classification (2000)Primary 53A25 Secondary 53B35
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