On the Twistor Spaces of Almost Hermitian Manifolds

Izu Vaisman

doi:10.1023/A:1006551225776

On the Twistor Spaces of Almost Hermitian Manifolds

Izu Vaisman

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study Grassmannian bundles script g sign_k (M) of analytical 2k-planes over an almost Hermitian manifold M²ⁿ, from the point of view of the generalized twistor spaces of [13], and with the method of the moving frame [9]. script g sign₁(M⁴) is the classical twistor space. We find four distinguished almost Hermitian structures, one of them being that of [13], and discuss their integrability and Kählerianity. For n = 2, we compute the corresponding Hermitian connections, and derive consequences about the corresponding first Chern classes.

Original language	English
Pages (from-to)	335-356
Number of pages	22
Journal	Annals of Global Analysis and Geometry
Volume	16
Issue number	4
DOIs	https://doi.org/10.1023/A:1006551225776
State	Published - 1998

Keywords

Bochner-flat Kähler manifolds
Twistor spaces

ASJC Scopus subject areas

Analysis
Political Science and International Relations
Geometry and Topology

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abstract = "We study Grassmannian bundles script g signk (M) of analytical 2k-planes over an almost Hermitian manifold M2n, from the point of view of the generalized twistor spaces of [13], and with the method of the moving frame [9]. script g sign1(M4) is the classical twistor space. We find four distinguished almost Hermitian structures, one of them being that of [13], and discuss their integrability and K{\"a}hlerianity. For n = 2, we compute the corresponding Hermitian connections, and derive consequences about the corresponding first Chern classes.",

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AB - We study Grassmannian bundles script g signk (M) of analytical 2k-planes over an almost Hermitian manifold M2n, from the point of view of the generalized twistor spaces of [13], and with the method of the moving frame [9]. script g sign1(M4) is the classical twistor space. We find four distinguished almost Hermitian structures, one of them being that of [13], and discuss their integrability and Kählerianity. For n = 2, we compute the corresponding Hermitian connections, and derive consequences about the corresponding first Chern classes.

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On the Twistor Spaces of Almost Hermitian Manifolds

Abstract

Keywords

ASJC Scopus subject areas

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