Metric geometries over the split quaternions
We give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples wi...
| Main Authors: | , , |
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| Format: | Journal article |
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2005
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| _version_ | 1826261556872085504 |
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| author | Dancer, A Jørgensen, H Swann, A |
| author_facet | Dancer, A Jørgensen, H Swann, A |
| author_sort | Dancer, A |
| collection | OXFORD |
| description | We give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaternionic Kähler metrics from indefinite real analytic conformal manifolds. We also indicate how the theory of toric varieties gives rise to constructions of hypersymplectic manifolds. |
| first_indexed | 2024-03-06T19:23:13Z |
| format | Journal article |
| id | oxford-uuid:1ad39f9c-1dea-48a8-8fe7-4de97e2e7cdb |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:23:13Z |
| publishDate | 2005 |
| record_format | dspace |
| spelling | oxford-uuid:1ad39f9c-1dea-48a8-8fe7-4de97e2e7cdb2022-03-26T10:56:58ZMetric geometries over the split quaternionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:1ad39f9c-1dea-48a8-8fe7-4de97e2e7cdbSymplectic Elements at Oxford2005Dancer, AJørgensen, HSwann, AWe give an overview of some recent results in hypersymplectic and para-quaternionic Kähler geometry, and introduce the notion of split three-Sasakian manifold. In particular, we discuss the twistor spaces and Swann bundles of para-quaternionic Kähler manifolds. These are used to classify examples with a fully homogeneous action of a semi-simple Lie group, and to construct distinct para-quaternionic Kähler metrics from indefinite real analytic conformal manifolds. We also indicate how the theory of toric varieties gives rise to constructions of hypersymplectic manifolds. |
| spellingShingle | Dancer, A Jørgensen, H Swann, A Metric geometries over the split quaternions |
| title | Metric geometries over the split quaternions |
| title_full | Metric geometries over the split quaternions |
| title_fullStr | Metric geometries over the split quaternions |
| title_full_unstemmed | Metric geometries over the split quaternions |
| title_short | Metric geometries over the split quaternions |
| title_sort | metric geometries over the split quaternions |
| work_keys_str_mv | AT dancera metricgeometriesoverthesplitquaternions AT jørgensenh metricgeometriesoverthesplitquaternions AT swanna metricgeometriesoverthesplitquaternions |