Curvature properties of twistor spaces of quaternionic Kähler manifolds
type: Item
instance of: scholarly article
title: Curvature properties of twistor spaces of quaternionic Kähler manifolds
zbMATH Open document ID: 0911.53019
DOI: 10.1007/BF01237595
author: Bogdan Alexandrov
author: Gueo Grantcharov
author: Stefan Ivanov
published in: Journal of Geometry
publication date: 1999-05-05T00:00:00Z
review text: The authors supply \((4n+2)\)-dimensional examples \((n>1)\) of strictly almost Kähler manifolds by studying natural almost Hermitian structures on twistor spaces of \(4n\)-dimensional quaternionic Kähler manifolds and show that some of them give negative answers to the questions raised by \textit{D. E. Blair} and \textit{S. Ianus} [Contemp. Math. 51, 23-29 (1986; Zbl 0591.53030)] and by \textit{A. Gray} [Tôhoku Math. J., II. Ser. 28, 601-612 (1976; Zbl 0351.53040)], respectively, of whether a compact almost Kähler manifold with Hermitian Ricci tensor or whose curvature tensor belongs to the class AH2 is Kähler. Negative answers to both of the questions were first given in dimension 6: to the first question by \textit{J. Davidov} and \textit{O. Muškarov} [Proc. Am. Math. Soc. 109, 1115-1120 (1990; Zbl 0704.53051)] and to the second question by \textit{J. Davidov}, \textit{O. Muškarov} and \textit{G. Grantcharov} [Ill. J. Math. 39, 627-634 (1995; Zbl 0844.53038)], respectively.
reviewed by: Kouei Sekigawa
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 1200017
zbMATH Keywords: twistor space
zbMATH Keywords: almost Kähler manifold
zbMATH Keywords: quaternionic Kähler manifold
zbMATH Keywords: curvature tensor
MaRDI profile type: Publication
cites work: Infinite Hankel matrices and generalized Caratheodory-Fejer and Riesz problems
cites work: Self-duality in four-dimensional Riemannian geometry
cites work: Lie groups and twistor spaces
cites work: Rigidity of nonnegatively curved compact quaternionic-Kähler manifolds
cites work: Twistor Spaces with Hermitian Ricci Tensor
cites work: Q3312978
cites work: Harmonic Mappings of Riemannian Manifolds
cites work: Integrability of Almost Kaehler Manifolds
cites work: Curvature identities for Hermitian and almost Hermitian manifolds
cites work: The sixteen classes of almost Hermitian manifolds and their linear invariants
cites work: Complex structures on quaternionic manifolds
cites work: Symplectic twistor spaces
cites work: Quaternionic Kaehler manifolds
cites work: Shorter Notes: Some Simple Examples of Symplectic Manifolds
cites work: Q4854053
description: scientific article; zbMATH DE number 1200017