CR-Geometry and Shearfree Lorentzian Geometry

Alekseevsky, Dmitri V.; Ganji, Masoud; Schmalz, Gerd

doi:10.1007/978-981-13-1672-2_2

Cited by 9 publications

(10 citation statements)

References 7 publications

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“…Thus, the charge conjugate of a spinor ν A 1 P S `will be denoted ν A when m is odd, and ν A 1 P S `when m is even. 3 Moreover, if ν A 1 is pure so is its charge conjugate. We define the real index of a pure spinor to be the real index of its associated null structure.…”

Section: 24mentioning

confidence: 99%

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Almost Robinson geometries

Fino¹,

Leistner²,

Taghavi-Chabert³

2021

Preprint

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We investigate the geometry of almost Robinson manifolds, Lorentzian analogues of 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.

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Section: 24mentioning

confidence: 99%

“…We do not touch on questions related to the curvature of almost Robinson manifolds, these being dealt with in [95]. Finally, we point out the recent articles [3,4] whose content overlaps with some aspects of the present article.…”

mentioning

confidence: 92%

Almost Robinson geometries

Fino¹,

Leistner²,

Taghavi-Chabert³

2021

Preprint

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“…Definition 3.1. [1] A shearfree congruence on an even-dimensional Lorentzian manifold (M, g) is a foliation by integral curves of a nowhere vanishing vector field k, such that (i) The vector field k is null, i.e. g(k, k) = 0.…”

Section: Shearfree Geometry and Cr Geometrymentioning

confidence: 99%

“…Here we mean by shearfree Lorentzian geometry a Lorentzian manifold (M, g) with a foliation by null-geodesics generated by a shearfree vector field k, that is, k is conformal Killing along on k ⊥ . See [1] for details.…”

Section: Introductionmentioning

confidence: 99%

On a construction of quasi-Einstein shearfree spacetimes

Ganji¹,

Schmalz²,

Sykes³

2020

Preprint

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In this article we prove that a certain class of smooth Sasakian manifolds admits lifts to 4-dimensional quasi-Einstein shearfree spacetimes of Petrov type II or D. This is related to an analogous result by Hill, Lewandowski and Nurowski [4] for general real-analytic CR manifolds. In particular, this holds for all tubular CR manifolds. Furthermore, we show that any Sasakian manifold with underlying Khler-Einstein manifold with non-zero Einstein constant has a lift to a shearfree Einstein metric of Petrov type II or D.

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“…An almost Robinson structure will be called shear-free almost Robinson structure if (cf. [1]) An interesting subclass of regular shear-free Kahler-Robinson manifolds is given by the Fefferman spaces which are some S 1 -principal bundles over strictly pseudoconvex CR manifolds. We briefly recall the construction of these spaces given in [3], [18].…”

Section: The Torsion Of ∇ Is Given Bymentioning

confidence: 99%