Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures
Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in a basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases...
| Main Authors: | , |
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| Format: | Journal article |
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Elsevier
2017
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| _version_ | 1797094710134702080 |
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| author | Dunajski, M Tod, P |
| author_facet | Dunajski, M Tod, P |
| author_sort | Dunajski, M |
| collection | OXFORD |
| description | Most known four-dimensional cohomogeneity-one Einstein metrics are diagonal in a basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non-diagonal Bianchi type VIII Einstein metrics with self-dual Weyl tensor. |
| first_indexed | 2024-03-07T04:17:48Z |
| format | Journal article |
| id | oxford-uuid:c9f9b72b-0dd3-4025-a1f5-982b51740f3c |
| institution | University of Oxford |
| last_indexed | 2024-03-07T04:17:48Z |
| publishDate | 2017 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:c9f9b72b-0dd3-4025-a1f5-982b51740f3c2022-03-27T07:03:59ZNon-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signaturesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c9f9b72b-0dd3-4025-a1f5-982b51740f3cSymplectic Elements at OxfordElsevier2017Dunajski, MTod, PMost known four-dimensional cohomogeneity-one Einstein metrics are diagonal in a basis defined by the left-invariant one-forms, though some essentially non-diagonal ones are known. We consider the problem of explicitly seeking non-diagonal Einstein metrics, and we find solutions which in some cases exhaust the possibilities. In particular we construct new examples of neutral signature non-diagonal Bianchi type VIII Einstein metrics with self-dual Weyl tensor. |
| spellingShingle | Dunajski, M Tod, P Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures |
| title | Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures |
| title_full | Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures |
| title_fullStr | Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures |
| title_full_unstemmed | Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures |
| title_short | Non-diagonal four-dimensional cohomogeneity-one Einstein metrics in various signatures |
| title_sort | non diagonal four dimensional cohomogeneity one einstein metrics in various signatures |
| work_keys_str_mv | AT dunajskim nondiagonalfourdimensionalcohomogeneityoneeinsteinmetricsinvarioussignatures AT todp nondiagonalfourdimensionalcohomogeneityoneeinsteinmetricsinvarioussignatures |