English

On the Geometry of Spaces of Oriented Geodesics

Differential Geometry 2020-11-19 v1

Abstract

Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space (other than the octonion hyperbolic plane), 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)Kaehler structure on L(M).

Keywords

Cite

@article{arxiv.0911.2602,
  title  = {On the Geometry of Spaces of Oriented Geodesics},
  author = {Dmitri V. Alekseevsky and Brendan Guilfoyle and Wilhelm Klingenberg},
  journal= {arXiv preprint arXiv:0911.2602},
  year   = {2020}
}

Comments

29 pages LaTEX