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Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
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G. Calvaruso
Published/Copyright:
November 28, 2008
Abstract
We determine, for all three-dimensional non-unimodular Lie groups equipped with a Lorentzian metric, the set of homogeneous geodesics through a point. Together with the results of [G. Calvaruso, Homogeneous structures on three-dimensional Lorentzian manifolds. J. Geom. Phys.57 (2007), 1279–1291. MR2287304 (2008b:53066) Zbl 1112.53051] and [G. Calvaruso, R. A. Marinosci, Homogeneous geodesics of three-dimensional unimodular Lorentzian Lie groups. Mediterr. J. Math.3 (2006), 467–481. MR2274738 Zbl pre05151042], this leads to the full classification of three-dimensional Lorentzian g.o. spaces and naturally reductive spaces.
Key words.: Lorentzian homogeneous spaces; homogeneous geodesics; naturally reductive spaces; g.o. spaces
Received: 2006-12-01
Published Online: 2008-11-28
Published in Print: 2008-October
© de Gruyter 2008
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Keywords for this article
Lorentzian homogeneous spaces;
homogeneous geodesics;
naturally reductive spaces;
g.o. spaces
Articles in the same Issue
- Homogeneous geodesics of non-unimodular Lorentzian Lie groups and naturally reductive Lorentzian spaces in dimension three
- Finite type Monge–Ampère foliations
- The horofunction boundary of the Hilbert geometry
- Counting the hyperplane sections with fixed invariants of a plane quintic – three approaches to a classical enumerative problem
- Totally non-real divisors in linear systems on smooth real curves
- Covers of Klein surfaces
- A classification of polarized manifolds by the sectional Betti number and the sectional Hodge number
- On reduced polytopes and antipodality
