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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| Дата: | 2013 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | 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 |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-149367 |
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dspace |
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irk-123456789-1493672019-02-22T01:23:30Z Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors Sheftel, M.B. Malykh, A.A. 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. 2013 Article 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. 1815-0659 2010 Mathematics Subject Classification: 35Q75; 83C15 DOI: http://dx.doi.org/10.3842/SIGMA.2013.075 http://dspace.nbuv.gov.ua/handle/123456789/149367 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
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. |
| format |
Article |
| author |
Sheftel, M.B. Malykh, A.A. |
| spellingShingle |
Sheftel, M.B. Malykh, A.A. Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Sheftel, M.B. Malykh, A.A. |
| author_sort |
Sheftel, M.B. |
| title |
Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors |
| title_short |
Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors |
| title_full |
Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors |
| title_fullStr |
Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors |
| title_full_unstemmed |
Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors |
| title_sort |
partner symmetries, group foliation and asd ricci-flat metrics without killing vectors |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149367 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT sheftelmb partnersymmetriesgroupfoliationandasdricciflatmetricswithoutkillingvectors AT malykhaa partnersymmetriesgroupfoliationandasdricciflatmetricswithoutkillingvectors |
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2023-05-20T17:32:50Z |
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2023-05-20T17:32:50Z |
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