Killing-Yano tensors and multi-hermitian structures
We show that the Euclidean Kerr-NUT-(A)dS metric in $2m$ dimensions locally admits $2^m$ hermitian complex structures. These are derived from the existence of a non-degenerate closed conformal Killing-Yano tensor with distinct eigenvalues. More generally, a conformal Killing-Yano tensor, provided it...
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| Format: | Journal article |
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2008
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| _version_ | 1826282258586140672 |
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| author | Mason, L Taghavi-Chabert, A |
| author_facet | Mason, L Taghavi-Chabert, A |
| author_sort | Mason, L |
| collection | OXFORD |
| description | We show that the Euclidean Kerr-NUT-(A)dS metric in $2m$ dimensions locally admits $2^m$ hermitian complex structures. These are derived from the existence of a non-degenerate closed conformal Killing-Yano tensor with distinct eigenvalues. More generally, a conformal Killing-Yano tensor, provided its exterior derivative satisfies a certain condition, algebraically determines $2^m$ almost complex structures that turn out to be integrable as a consequence of the conformal Killing-Yano equations. In the complexification, these lead to $2^m$ maximal isotropic foliations of the manifold and, in Lorentz signature, these lead to two congruences of null geodesics. These are not shear-free, but satisfy a weaker condition that also generalizes the shear-free condition from 4-dimensions to higher-dimensions. In odd dimensions, a conformal Killing-Yano tensor leads to similar integrable distributions in the complexification. We show that the recently discovered 5-dimensional solution of Lu, Mei and Pope also admits such integrable distributions, although this does not quite fit into the story as the obvious associated two-form is not conformal Killing-Yano. We give conditions on the Weyl curvature tensor imposed by the existence of a non-degenerate conformal Killing-Yano tensor; these give an appropriate generalization of the type D condition on a Weyl tensor from four dimensions. |
| first_indexed | 2024-03-07T00:41:07Z |
| format | Journal article |
| id | oxford-uuid:8311a7ee-9973-432d-bcae-fffb6d2d861d |
| institution | University of Oxford |
| last_indexed | 2024-03-07T00:41:07Z |
| publishDate | 2008 |
| record_format | dspace |
| spelling | oxford-uuid:8311a7ee-9973-432d-bcae-fffb6d2d861d2022-03-26T21:41:47ZKilling-Yano tensors and multi-hermitian structuresJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8311a7ee-9973-432d-bcae-fffb6d2d861dSymplectic Elements at Oxford2008Mason, LTaghavi-Chabert, AWe show that the Euclidean Kerr-NUT-(A)dS metric in $2m$ dimensions locally admits $2^m$ hermitian complex structures. These are derived from the existence of a non-degenerate closed conformal Killing-Yano tensor with distinct eigenvalues. More generally, a conformal Killing-Yano tensor, provided its exterior derivative satisfies a certain condition, algebraically determines $2^m$ almost complex structures that turn out to be integrable as a consequence of the conformal Killing-Yano equations. In the complexification, these lead to $2^m$ maximal isotropic foliations of the manifold and, in Lorentz signature, these lead to two congruences of null geodesics. These are not shear-free, but satisfy a weaker condition that also generalizes the shear-free condition from 4-dimensions to higher-dimensions. In odd dimensions, a conformal Killing-Yano tensor leads to similar integrable distributions in the complexification. We show that the recently discovered 5-dimensional solution of Lu, Mei and Pope also admits such integrable distributions, although this does not quite fit into the story as the obvious associated two-form is not conformal Killing-Yano. We give conditions on the Weyl curvature tensor imposed by the existence of a non-degenerate conformal Killing-Yano tensor; these give an appropriate generalization of the type D condition on a Weyl tensor from four dimensions. |
| spellingShingle | Mason, L Taghavi-Chabert, A Killing-Yano tensors and multi-hermitian structures |
| title | Killing-Yano tensors and multi-hermitian structures |
| title_full | Killing-Yano tensors and multi-hermitian structures |
| title_fullStr | Killing-Yano tensors and multi-hermitian structures |
| title_full_unstemmed | Killing-Yano tensors and multi-hermitian structures |
| title_short | Killing-Yano tensors and multi-hermitian structures |
| title_sort | killing yano tensors and multi hermitian structures |
| work_keys_str_mv | AT masonl killingyanotensorsandmultihermitianstructures AT taghavichaberta killingyanotensorsandmultihermitianstructures |