Bächtold, M (2007). Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution. Differential Geometry and its Applications, 25(2):167-176.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > Analysis
Physical Sciences > Geometry and Topology Physical Sciences > Computational Theory and Mathematics |
| Language: | English |
| Date: | April 2007 |
| Deposited On: | 24 Mar 2010 13:46 |
| Last Modified: | 28 Jun 2022 07:44 |
| Publisher: | Elsevier |
| ISSN: | 0926-2244 |
| OA Status: | Hybrid |
| 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 |
Bächtold, M