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).
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The first author was supported by the Leverhulme Trust, EM/9/2005/0069.
An erratum to this article is available at http://dx.doi.org/10.1007/s10455-016-9515-3.
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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
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DOI: https://doi.org/10.1007/s10455-011-9261-5
Keywords
- Space of geodesics
- Homogeneous manifolds
- Pseudo-Riemannian metrics
- Symplectic structures
- Kähler structures