On the geometry of spaces of oriented geodesics.

Alekseevsky, D.V.; Guilfoyle, B.; Klingenberg, W.

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).

Citation

Alekseevsky, D., Guilfoyle, B., & Klingenberg, W. (2011). On the geometry of spaces of oriented geodesics. Annals of Global Analysis and Geometry, 40(4), 389-409. https://doi.org/10.1007/s10455-011-9261-5

• Journal Article Type: Article
• Publication Date: 2011-12
• Deposit Date: Dec 21, 2011
• Journal: Annals of Global Analysis and Geometry
• Print ISSN: 0232-704X
• Electronic ISSN: 1572-9060
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 4
• Pages: 389-409
• DOI: https://doi.org/10.1007/s10455-011-9261-5
• Public URL: https://durham-repository.worktribe.com/output/1500842