Almost Robinson geometries
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2021
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929608613429248 |
|---|---|
| author | Fino, Anna Leistner, Thomas Taghavi-Chabert, Arman |
| author_facet | Fino, Anna Leistner, Thomas Taghavi-Chabert, Arman |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_05634 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Almost Robinson geometries Fino, Anna Leistner, Thomas Taghavi-Chabert, Arman Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 53C50, 53C10 (Primary) 53B30, 53C18 (Secondary) 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. |
| title | Almost Robinson geometries |
| topic | Differential Geometry General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics 53C50, 53C10 (Primary) 53B30, 53C18 (Secondary) |
| url | https://arxiv.org/abs/2102.05634 |