Locally homogeneous pseudo-Riemannian manifolds
type: Item
instance of: scholarly article
title: Locally homogeneous pseudo-Riemannian manifolds
zbMATH Open document ID: 0832.53017
DOI: 10.1016/0393-0440(94)00040-B
author: Vic Patrangenaru
published in: Journal of Geometry and Physics
publication date: 1996-02-26T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 806360
zbMATH Keywords: locally homogeneous pseudo-Riemannian manifolds
zbMATH Keywords: Cartan triples
Wikidata QID: Q115363099
reviewed by: Lieven Vanhecke
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 806360