On the geometry of spaces of oriented geodesics

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,...

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Veröffentlicht in:	Annals of global analysis and geometry 2011-12, Vol.40 (4), p.389-409
Hauptverfasser:	Alekseevsky, Dmitri V., Guilfoyle, Brendan, Klingenberg, Wilhelm
Format:	Artikel
Sprache:	eng
Schlagworte:	Analysis Curvature Differential Geometry Euclidean space Geometry Global Analysis and Analysis on Manifolds Invariants Lie groups Manifolds Mathematical analysis Mathematical Physics Mathematics Mathematics and Statistics Original Paper Studies
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Beschreibung
Zusammenfassung:	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 ).
ISSN:	0232-704X 1572-9060
DOI:	10.1007/s10455-011-9261-5