On the Ricci operator of locally homogeneous Lorentzian 3-manifolds
type: Item
instance of: scholarly article
title: On the Ricci operator of locally homogeneous Lorentzian 3-manifolds
zbMATH Open document ID: 1180.53070
author: Oldřich Kowalski
author: Giovanni Calvaruso
published in: Central European Journal of Mathematics
publication date: 2009-11-02T00:00:00Z
review text: Lorentzian 3-manifolds split into four possible Segre types. In the paper the possible Segre types together with the possible eigenvalues of the Ricci tensor are determined for locally homogeneous (or curvature-homogeneous) Lorentzian 3-manifolds. BY previous work of the first author, the problem can be reduced to the case of a locally symmetric space or a 3-dimensional Lie group with a left invariant Lorentzian metric.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 5624218
zbMATH Keywords: Segre type
zbMATH Keywords: Ricci tensor
zbMATH Keywords: symmetric space
reviewed by: Wolfgang Kühnel
MaRDI profile type: Publication
full work available at URL: s11533-008-0061-5
OpenAlex ID: W2061992919
cites work: Three-dimensional Lorentzian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3
cites work: On curvature homogeneous three-dimensional Lorentzian manifolds
cites work: Three-dimensional Lorentz metrics and curvature homogeneity of order one
cites work: Homogeneous structures on three-dimensional Lorentzian manifolds
cites work: Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds
cites work: Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues
cites work: Three-dimensional homogeneous Lorentzian metrics with prescribed Ricci tensor
cites work: Three-dimensional Lorentz manifolds admitting a parallel null vector field
cites work: Q4400072
cites work: Q3141982
cites work: On Ricci eigenvalues of locally homogeneous Riemann 3-manifolds
cites work: On Riemannian 3-manifolds with distinct constant Ricci eigenvalues
cites work: Curvatures of left invariant metrics on Lie groups
cites work: Q3312869
cites work: Left-invariant Lorentz metrics on Lie groups
cites work: Lorentz metrics on unimodular Lie groups of dimension three
DOI: 10.2478/S11533-008-0061-5
description: scientific article; zbMATH DE number 5624218