Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution
type: Item
instance of: scholarly article
title: Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution
zbMATH Open document ID: 1123.53023
author: Michael Bächtold
published in: Differential Geometry and its Applications
publication date: 2007-07-23T00:00:00Z
review text: In the present article the author finds all metrics \(g\) in a \(4\)-dimensional manifold of any signature with vanishing Ricci tensor, that satisfy three conditions: (i) \(g\) allows a Lie algebra of Killing vector fields with \(2\)-dimensional orbits, (ii) the tensor \(g\) degenerates when restricted to the orbits, and (iii) the distribution orthogonal to the orbits is not integrable. The main result is that there exists only one (up to sign), Ricci flat metric.
reviewed by: Andreas Arvanitoyeorgos
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 5173593
zbMATH Keywords: Ricci flat metrics
zbMATH Keywords: Einstein metrics
zbMATH Keywords: Killing algebra
zbMATH Keywords: null orbits
zbMATH Keywords: Kleinian metrics
MaRDI profile type: Publication
full work available at URL: j.difgeo.2006.08.006
OpenAlex ID: W2118896508
Wikidata QID: Q115357809
cites work: Ricci flat 4-metrics with bidimensional null orbits
cites work: Q4238949
cites work: Vacuum Einstein metrics with bidimensional Killing leaves. II: Global aspects.
DOI: 10.1016/J.DIFGEO.2006.08.006
description: scientific article; zbMATH DE number 5173593