Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors
We demonstrate how a combination of our recently developed methods of partner symmetries, symmetry reduction in group parameters and a new version of the group foliation method can produce noninvariant solutions of complex Monge-Ampère equation (CMA) and provide a lift from invariant solutions of CM...
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| Datum: | 2013 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут математики НАН України
2013
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/149367 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors / M.B. Sheftel, A.A. Malykh // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 28 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | We demonstrate how a combination of our recently developed methods of partner symmetries, symmetry reduction in group parameters and a new version of the group foliation method can produce noninvariant solutions of complex Monge-Ampère equation (CMA) and provide a lift from invariant solutions of CMA satisfying Boyer-Finley equation to non-invariant ones. Applying these methods, we obtain a new noninvariant solution of CMA and the corresponding Ricci-flat anti-self-dual Einstein-Kähler metric with Euclidean signature without Killing vectors, together with Riemannian curvature two-forms. There are no singularities of the metric and curvature in a bounded domain if we avoid very special choices of arbitrary functions of a single variable in our solution. This metric does not describe gravitational instantons because the curvature is not concentrated in a bounded domain. |
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