Annals of Global Analysis and Geometry

, Volume 40, Issue 4, pp 389–409

On the geometry of spaces of oriented geodesics

  • Dmitri V. Alekseevsky
  • Brendan Guilfoyle
  • Wilhelm Klingenberg
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

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).

Keywords

Space of geodesics Homogeneous manifolds Pseudo-Riemannian metrics Symplectic structures Kähler structures 

Mathematics Subject Classification (2000)

Primary 53A25 Secondary 53B35 

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Dmitri V. Alekseevsky
    • 1
  • Brendan Guilfoyle
    • 2
  • Wilhelm Klingenberg
    • 3
  1. 1.School of Mathematics and Maxwell Insitute for Mathematical Sciences, The Kings Buildings, JCMBUniversity of EdinburghEdinburghUK
  2. 2.Department of Computing and MathematicsIT TraleeTralee County KerryIreland
  3. 3.School of Mathematical SciencesUniversity of DurhamDurhamUK