A null geodesic orbit space whose null orbits require a reparametrization. (English) Zbl 1192.53065

Calvaruso, Giovanni; Dušek, Zdeněk

Mladenov, Ivaïlo M. (ed.), Proceedings of the 9th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 8–13, 2007. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-42-4/pbk). 167-174 (2008).

Summary: We exhibit an example of a homogeneous Lorentzian manifold \(G/H\) whose homogeneous geodesics form just the light-cone and a hyperplane in the tangent space. For all light-like homogeneous geodesics, the natural parameter of the orbit is not the affine parameter of the geodesic.
For the entire collection see [Zbl 1154.17001].

MSC:

53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C22	Geodesics in global differential geometry

Keywords:

reductive homogeneous plane wave; almost geodesic orbit space; homogeneous geodesics; geodesic graph; geodesic vector