Optical geometries and related structures
type: Item
instance of: scholarly article
title: Optical geometries and related structures
zbMATH Open document ID: 0849.53014
DOI: 10.1016/0393-0440(95)00012-7
published in: Journal of Geometry and Physics
publication date: 1996-11-10T00:00:00Z
review text: This article contains a discussion of two optical geometries on the space of all (principal) null directions \(P\) of a four-dimensional Lorentzian manifold \(M\). One of these geometries is always non-integrable, while the other is integrable if and only if \(M\) is conformally flat. Various conditions and properties of \(P\) are analyzed and related to properties on \(M\), and an analogy between optical and Hermitian geometries is discussed. Finally, it is shown that the construction of optical geometries on \(P\) is a Lorentzian analogue of the \textit{M. F. Atiyah}, \textit{N. J. Hitchin} and \textit{I. M. Singer} construction [Proc. R. Soc. Lond., Ser. A 362, 425-461 (1978; Zbl 0389.53011)], of almost Hermitian structures on the twistor space of a four-dimensional Euclidean manifold.
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53B35
Mathematics Subject Classification ID: 83C60
zbMATH DE Number: 880621
zbMATH Keywords: space of principal null directions
zbMATH Keywords: optical geometries
zbMATH Keywords: Hermitian geometries
author: Pawel Nurowski
reviewed by: Joseph D. Zund
MaRDI profile type: Publication
full work available at URL: 0393-0440(95)00012-7
OpenAlex ID: W2000102082
cites work: Self-duality in four-dimensional Riemannian geometry
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cites work: Correction to 'Monge-Ampère equations, the Bergman kernel, and geometry of pseudoconvex domains'
cites work: Degeneracy in loop variables
cites work: Q5721035
cites work: A generalised Kerr-Robinson theorem
cites work: Q3896182
cites work: Simple spinors and real structures
cites work: On the Fefferman class of metrics associated with a three-dimensional CR space
cites work: Twistor equation in a curved spacetime
cites work: Einstein's equations and realizability of CR manifolds
cites work: Summary of session A2: complex methods, twistors and connection variables
cites work: Complex analytic coordinates in almost complex manifolds
cites work: A spinor approach to general relativity
cites work: Twistor Algebra
cites work: Physical space-time and nonrealizable 𝐶𝑅-structures
cites work: Q3324593
cites work: Q3719430
cites work: Properties of shear-free congruences of null geodesics
cites work: Type N vacuum space-times as special functions in \(\mathbb{C}^2\)
cites work: On the Robinson theorem and shearfree geodesic null congruences
cites work: Deformations of the Hodge map and optical geometry
cites work: Q4857196
Wikidata QID: Q126085735
description: scientific article; zbMATH DE number 880621