On the geometry of spaces of oriented geodesics |
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| Authors: | Dmitri V Alekseevsky Brendan Guilfoyle Wilhelm Klingenberg |
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| Institution: | 1.School of Mathematics and Maxwell Insitute for Mathematical Sciences, The Kings Buildings, JCMB,University of Edinburgh,Edinburgh,UK;2.Department of Computing and Mathematics,IT Tralee,Tralee County Kerry,Ireland;3.School of Mathematical Sciences,University of Durham,Durham,UK |
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| Abstract: | 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). |
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