On the Geometry of Spaces of Oriented Geodesics.

Authors

Dmitri V. Alekseevsky, School of Mathematics and Maxwell Insitute for Mathematical Sciences, The Kings Buildings, JCMB, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ,UK.
Brendan Guilfoyle, Department of Computing and Mathematics, IT Tralee, Clash, Tralee, County Kerry, Ireland.Follow
Wilhelm Klingenberg, School of Mathematical Sciences, University of Durham, Durham DH1 3LE, UK.

Document Type

Article

Publication Details

Annals of Global Analysis and Geometry

© 2011 The Authors.

Abstract

Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space other than OH2 , 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)K¨ahler structure on L(M).

Recommended Citation

Alekseevsky, D.V., Guilfoyle, B. & Klingenberg, W. On the geometry of spaces of oriented geodesics. Ann Glob Anal Geom 40, 389–409 (2011). https://doi.org/10.1007/s10455-011-9261-5