Locally homogeneous pseudo-Riemannian manifolds
Locally homogeneous Riemannian manifolds may be studied by means of homogeneous structures and infinitesimal models. In his earlier work the author also studied these manifolds by using Cartan triples. The theory of homogeneous structures has been extended by Gadea and Oubiña to the case of locally homogeneous pseudo-Riemannian manifolds. In this paper the author extends the method of Cartan triples to the pseudo-Riemannian case and studies in detail the 3-dimensional Lorentz case. In the second part of the paper he uses these triples to construct several interesting examples such as 5-dimensional locally homogeneous pseudo-Riemannian manifolds which are not locally isometric to a homogeneous space (such examples are already known in the Riemannian case) and 3-dimensional nonsymmetric examples modelled on a symmetric space, i.e. examples with the same curvature tensor as that of a symmetric space.
locally homogeneous pseudo-Riemannian manifolds
scientific article; zbMATH DE number 806360