Original Paper

Annals of Global Analysis and Geometry

, Volume 40, Issue 4, pp 389-409

First online:

On the geometry of spaces of oriented geodesics

  • Dmitri V. AlekseevskyAffiliated withSchool of Mathematics and Maxwell Insitute for Mathematical Sciences, The Kings Buildings, JCMB, University of Edinburgh
  • , Brendan GuilfoyleAffiliated withDepartment of Computing and Mathematics, IT Tralee Email author 
  • , Wilhelm KlingenbergAffiliated withSchool of Mathematical Sciences, University of Durham

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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).

Keywords

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

Mathematics Subject Classification (2000)

Primary 53A25 Secondary 53B35