On the Twistor Spaces of Almost Hermitian Manifolds

Author: Vaisman I.

Source: Annals of Global Analysis and Geometry, Volume 16, Number 4, August 1998 , pp. 335-356(22)

Publisher: Springer

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Abstract:

We study Grassmannian bundles G_k(M) of analytical 2k-planes over an almost Hermitian manifold M^2n, from the point of view of the generalized twistor spaces of [13], and with the method of the moving frame [9]. G_1(M^4) 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.

Keywords: Bochner-flat Kähler manifolds; twistor spaces

Language: English

Document Type: Regular paper

Affiliations: 1: Department of Mathematics, University of Haifa, Mount Carmel, 31905 Haifa, Israel (E-mail: vaisman@math.haifa.ac.il)

Publication date: 1998-08-01