Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues
type: Item
instance of: scholarly article
title: Pseudo-Riemannian 3-manifolds with prescribed distinct constant Ricci eigenvalues
zbMATH Open document ID: 1153.53053
author: Giovanni Calvaruso
published in: Differential Geometry and its Applications
publication date: 2008-06-25T00:00:00Z
review text: The Riemannian curvature homogeneous three-spaces have been intensively studied. In his papers [J. Math. Phys. 37, No.~8, 4062--4075 (1996; Zbl 0866.53026) and ibid. 38, No.~2, 1000--1013 (1997; Zbl 0876.53042)], \textit{P. Bueken} studied three-dimensional curvature homogeneous Lorentzian spaces. The author of this paper studies three-dimensional pseudo-Riemannian manifolds having distinct constant principal Ricci curvatures. Also, homogeneous and non-homogeneous pseudo-Riemannian metrics in \(\mathbb R^3\) are explicitly constructed, having prescribed principal Ricci curvatures.
reviewed by: Constantin Călin
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 5292514
zbMATH Keywords: pseudo-Riemannian manifolds
zbMATH Keywords: Ricci eingevalues
MaRDI profile type: Publication
full work available at URL: j.difgeo.2007.11.031
OpenAlex ID: W2063613537
Wikidata QID: Q115357620
cites work: Q4379530
cites work: Three-dimensional Riemannian manifolds with constant principal Ricci curvatures ρ1=ρ2≠ρ3
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: Examples of curvature homogeneous Lorentz metrics
cites work: Homogeneous structures on three-dimensional Lorentzian manifolds
cites work: Einstein-like metrics on three-dimensional homogeneous Lorentzian manifolds
cites work: Three-dimensional Lorentz manifolds admitting a parallel null vector field
cites work: Q4400072
cites work: Complete curvature homogeneous pseudo-Riemannian manifolds
cites work: A classification of Riemannian 3-manifolds with constant principal ricci curvaturesρ1= ρ2≠ ρ3
cites work: On Ricci eigenvalues of locally homogeneous Riemann 3-manifolds
cites work: On Riemannian 3-manifolds with distinct constant Ricci eigenvalues
cites work: Classification of Riemannian 3-manifolds with distinct constant principal Ricci curvatures
cites work: Q5465267
cites work: Curvatures of left invariant metrics on Lie groups
cites work: Q3312869
cites work: Lorentz metrics on unimodular Lie groups of dimension three
cites work: Q4129415
cites work: Infinitesimally homogeneous spaces
cites work: Q5337746
cites work: A characterization of locally homogeneous Riemann manifolds of dimension 3
DOI: 10.1016/J.DIFGEO.2007.11.031
description: scientific article; zbMATH DE number 5292514