The complex Goldberg-Sachs theorem in higher dimensions
type: Item
instance of: scholarly article
title: The complex Goldberg-Sachs theorem in higher dimensions
zbMATH Open document ID: 1252.53086
author: Arman Taghavi-Chabert
published in: Journal of Geometry and Physics
publication date: 2012-05-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1107.2283
review text: This paper presents a comprehensive study of the geometric properties of some holomorphic distributions of totally null \(m\)-planes on complex Riemannian manifolds of certain dimensions. The author finds algebraic conditions for the Weyl tensor and the Cotton-York tensor which guarantee the integrability of the distribution, and in odd dimensions, of its orthogonal complement. It is shown that these results generalize the Petrov classification of the (anti-)self-dual part of the complex Weyl tensor and the complex Goldberg-Sachs theorem. In addition, higher dimensional analogues of the Petrov type \(D\) condition are defined and the results are adapted to real smooth pseudo-Riemannian manifolds. The applications to Hermitian geometry and Robinson (or optical) geometry are discussed.
reviewed by: Raina Ivanova
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C25
zbMATH DE Number: 6031296
zbMATH Keywords: integrability of distributions
zbMATH Keywords: null foliations
zbMATH Keywords: curvature prescription
zbMATH Keywords: complex geometry
zbMATH Keywords: conformal geometry
zbMATH Keywords: twistor geometry
MaRDI profile type: Publication
OpenAlex ID: W2149129969
arXiv ID: 1107.2283
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DOI: 10.1016/J.GEOMPHYS.2012.01.012
description: scientific article; zbMATH DE number 6031296