Left-invariant Riemannian metrics on four-dimensional nonunimodular Lie groups with zero-divergence Weyl tensor
type: Item
instance of: scholarly article
title: Left-invariant Riemannian metrics on four-dimensional nonunimodular Lie groups with zero-divergence Weyl tensor
zbMATH Open document ID: 1208.53058
DOI: 10.1134/S1064562410030154
author: D. S. Voronov
author: E. D. Rodionov
published in: Doklady Mathematics
publication date: 2010-12-08T00:00:00Z
review text: A Riemannian manifold \((M,g)\) of dimension \(n\geq 4\) is called a \(C\)-space if div\(\,W=0\) where \(W\) denotes the Weyl tensor. Due to the homogeneity property, the study of the divergence of the Weyl tensor on Lie groups reduces to a study at the Lie algebra level. The aim of this work is to determine the four-dimensional nonunimodular Lie groups which are \(C\)-spaces. The key is to find a convenient basis, an idea based on previous works. The resulting Lie algebras are presented in a table. Even though several references are given, the corresponding proofs are not written out explicitly, which makes the understanding of the used tools very difficult.
reviewed by: Gabriela Paola Ovando
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 22E25
zbMATH DE Number: 5824795
zbMATH Keywords: left invariant metrics
zbMATH Keywords: zero-divergence Weyl tensor
zbMATH Keywords: four-dimensional nonunimodular Lie groups
Wikidata QID: Q115247483
MaRDI profile type: Publication
cites work: On harmonic tensors on three-dimensional Lie groups with left-invariant Riemannian metric
cites work: Q5333687
cites work: Conformal Einstein spaces in \(n\)-dimensions
full work available at URL: s1064562410030154
OpenAlex ID: W2032128664
description: scientific article; zbMATH DE number 5824795