Almost contact structures on the set of rational curves in a 4-dimensional twistor space
type: Item
instance of: scholarly article
title: Almost contact structures on the set of rational curves in a 4-dimensional twistor space
arXiv ID: 2206.13151
author: Michifumi Teruya
published in: Kodai Mathematical Journal
publication date: 2024-01-05T00:00:00Z
full work available at URL: https://arxiv.org/abs/2206.13151
full work available at URL: kmj46306.full
review text: In complete analogy to the Penrose correspondence between 4-dimensional Riemannian manifolds and complex 3-manifolds, the author describes a possible definition of a 4-dimensional twistor space and of a 5-dimensional complex almost contact manifold parametrizing the holomorphic deformations of the twistor line. After describing the geometry of such spaces, the author proves an analogue of the well known theorem by Atiyah, Hitchin and Singer, see [\textit{M. F. Atiyah} et al., Proc. R. Soc. Lond., Ser. A 362, 425--461 (1978; Zbl 0389.53011)], showing that under natural conditions on the curvature of the underlying manifold there exists a 4-dimensional twistor space fibering over it and satisfying all the given conditions. The author then discusses several examples. In particular, it is shown that the 4-dimensional twistor space introduced by \textit{G. Ren} and \textit{W. Wang}, [J. Geom. Phys. 183, Article ID 104699, 14 p. (2023; Zbl 1506.53062)] and the one defined by \textit{M. Itoh}, [J. Math. Phys. 43, No. 7, 3783--3797 (2003; Zbl 1060.53057)] are morally identical.
reviewed by: Amedeo Altavilla
Mathematics Subject Classification ID: 53C28
Mathematics Subject Classification ID: 53D15
zbMATH DE Number: 7784611
zbMATH Keywords: twistor space
zbMATH Keywords: almost contact structure
zbMATH Keywords: contact metric structure
zbMATH Keywords: \(K\)-contact structure
MaRDI profile type: Publication
OpenAlex ID: W4387337586
DOI: 10.2996/KMJ46306
description: scientific article; zbMATH DE number 7784611