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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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2013 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2013
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| Онлайн доступ: | https://nasplib.isofts.kiev.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| _version_ | 1862544267373707264 |
|---|---|
| author | Sheftel, M.B. Malykh, A.A. |
| author_facet | Sheftel, M.B. Malykh, A.A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-11-24T23:53:59Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149367 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T23:53:59Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Sheftel, M.B. Malykh, A.A. 2019-02-21T07:22:47Z 2019-02-21T07:22:47Z 2013 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 https://nasplib.isofts.kiev.ua/handle/123456789/149367 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. We thank our referees for their encouragement and criticism which hopefully improved our
 paper. The research of M.B. Sheftel was supported in part by the research grant from Bo˘gazi¸ci
 University Scientific Research Fund (BAP), research project No. 6324. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors Article published earlier |
| spellingShingle | Partner Symmetries, Group Foliation and ASD Ricci-Flat Metrics without Killing Vectors Sheftel, M.B. Malykh, A.A. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149367 |
| work_keys_str_mv | AT sheftelmb partnersymmetriesgroupfoliationandasdricciflatmetricswithoutkillingvectors AT malykhaa partnersymmetriesgroupfoliationandasdricciflatmetricswithoutkillingvectors |