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,...

Full description

Saved in:
Bibliographic Details
Published in:Annals of global analysis and geometry 2011-12, Vol.40 (4), p.389-409
Main Authors: Alekseevsky, Dmitri V., Guilfoyle, Brendan, Klingenberg, Wilhelm
Format: Article
Language:English
Subjects:
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
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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