Ricci flat metrics with bidimensional null orbits and non-integrable orthogonal distribution |
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Authors: | Michael Bächtold |
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Institution: | Mathematik Departement, ETH, Zürich, Switzerland |
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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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Keywords: | 53C25 53C50 53C30 |
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