Almost Robinson geometries
| dc.contributor.author | Fino, A. | |
| dc.contributor.author | Leistner, T. | |
| dc.contributor.author | Taghavi-Chabert, A. | |
| dc.date.issued | 2023 | |
| dc.description.abstract | We investigate the geometry of almost Robinson manifolds, Lorentzian analogues of almost Hermitian manifolds, defined by Nurowski and Trautman as Lorentzian manifolds of even dimension equipped with a totally null complex distribution of maximal rank. Associated to such a structure, there is a congruence of null curves, which, in dimension four, is geodesic and non-shearing if and only if the complex distribution is involutive. Under suitable conditions, the distribution gives rise to an almost Cauchy–Riemann structure on the leaf space of the congruence. We give a comprehensive classification of such manifolds on the basis of their intrinsic torsion. This includes an investigation of the relation between an almost Robinson structure and the geometric properties of the leaf space of its congruence. We also obtain conformally invariant properties of such a structure, and we finally study an analogue of so-called generalised optical geometries as introduced by Robinson and Trautman. | |
| dc.description.statementofresponsibility | Anna Fino, Thomas Leistner, Arman Taghavi-Chabert | |
| dc.identifier.citation | Letters in Mathematical Physics, 2023; 113(3):56-1-56-103 | |
| dc.identifier.doi | 10.1007/s11005-023-01667-x | |
| dc.identifier.issn | 0377-9017 | |
| dc.identifier.issn | 1573-0530 | |
| dc.identifier.orcid | Leistner, T. [0000-0002-8837-5215] | |
| dc.identifier.uri | https://hdl.handle.net/2440/138715 | |
| dc.language.iso | en | |
| dc.publisher | Springer Science and Business Media LLC | |
| dc.relation.grant | http://purl.org/au-research/grants/arc/DP190102360 | |
| dc.rights | © The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. | |
| dc.source.uri | https://doi.org/10.1007/s11005-023-01667-x | |
| dc.subject | Lorentzian manifolds; Almost Robinson structures; G-structure; Intrinsic torsion; Congruences of null geodesics; Conformal geometry; Almost CR structures | |
| dc.title | Almost Robinson geometries | |
| dc.type | Journal article | |
| pubs.publication-status | Published |
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