Annals of Global Analysis and Geometry

, Volume 40, Issue 4, pp 389–409

On the geometry of spaces of oriented geodesics


  • Dmitri V. Alekseevsky
    • School of Mathematics and Maxwell Insitute for Mathematical Sciences, The Kings Buildings, JCMBUniversity of Edinburgh
    • Department of Computing and MathematicsIT Tralee
  • Wilhelm Klingenberg
    • School of Mathematical SciencesUniversity of Durham
Original Paper

DOI: 10.1007/s10455-011-9261-5

Cite this article as:
Alekseevsky, D.V., Guilfoyle, B. & Klingenberg, W. Ann Glob Anal Geom (2011) 40: 389. doi:10.1007/s10455-011-9261-5


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).


Space of geodesicsHomogeneous manifoldsPseudo-Riemannian metricsSymplectic structuresKähler structures

Mathematics Subject Classification (2000)

Primary 53A25Secondary 53B35
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© Springer Science+Business Media B.V. 2011