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Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution


Bächtold, M (2007). Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution. Differential Geometry and its Applications, 25(2):167-176.

Abstract

We study Ricci flat 4-metrics of any signature under the assumption that they allow a Lie algebra of Killing fields with 2-dimensional orbits along which the metric degenerates and whose orthogonal distribution is not integrable. It turns out that locally there is a unique (up to a sign) metric which satisfies the conditions. This metric is of signature (++−−) and, moreover, homogeneous possessing a 6-dimensional symmetry algebra.

Abstract

We study Ricci flat 4-metrics of any signature under the assumption that they allow a Lie algebra of Killing fields with 2-dimensional orbits along which the metric degenerates and whose orthogonal distribution is not integrable. It turns out that locally there is a unique (up to a sign) metric which satisfies the conditions. This metric is of signature (++−−) and, moreover, homogeneous possessing a 6-dimensional symmetry algebra.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:April 2007
Deposited On:24 Mar 2010 13:46
Last Modified:05 Apr 2016 13:54
Publisher:Elsevier
ISSN:0926-2244
Publisher DOI:https://doi.org/10.1016/j.difgeo.2006.08.006
Related URLs:http://www.zentralblatt-math.org/zmath/en/advanced/?q=an:1123.53023&format=complete

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