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On the Geometry of Spaces of Oriented Geodesics

Dmitri V. Alekseevsky, Brendan Guilfoyle and Wilhelm Klingenberg
Arxiv ID: 0911.2602Last updated: 11/19/2020
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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