Non-Reductive Four Dimensional Homogeneous Pseudo-Riomannian Mani-Folds
Document Type
Article
Journal/Book Title/Conference
Canadian Journal of Math
Volume
58
Issue
2
Publication Date
2006
First Page
282
Last Page
311
Abstract
A method, due to Élie Cartan, is used to give an algebraic classification of the non-reductive homogeneous pseudo-Riemannian manifolds of dimension four. Only one case with Lorentz signature can be Einstein without having constant curvature, and two cases with (2, 2) signature are Einstein of which one is Ricci-flat. If a four-dimensional non-reductive homogeneous pseudo-Riemannian manifold is simply connected, then it is shown to be diffeomorphic to ℝ 4. All metrics for the simply connected non-reductive Einstein spaces are given explicitly. There are no non-reductive pseudo-Riemannian homogeneous spaces of dimension two and none of dimension three with connected isotropy subgroup.
Recommended Citation
Non-reductive four dimensional homogeneous pseudo-Riemannian Mani- folds, M.E. Fels, A.G. Renner, Canadian Journal of Math., 58(2), 2006, 282-311.
