Nearly Kähler manifolds with vanishing Tricerri-Vanhecke Bochner curvature tensor
type: Item
instance of: scholarly article
title: Nearly Kähler manifolds with vanishing Tricerri-Vanhecke Bochner curvature tensor
zbMATH Open document ID: 1167.53030
author: J. Martínez
published in: Differential Geometry and its Applications
publication date: 2009-04-16T00:00:00Z
review text: The authors give a local classification of nearly Kähler manifolds \((M,g,J)\) with vanishing Tricieri-Vanhecke (TV) curvature Bochner type tensor \(B(R)\). For Kähler manifolds the tensor \(B(R)\) coincides with the Bochner tensor. The authors prove that there do not exist TV Bochner flat strict nearly Kähler manifolds of dimension \(2n\geq 10\). The main result of the paper is the following theorem: Theorem. Let \((M,g,J)\) be a \(2n\geq 6\)-dimensional TV Bochner flat strict nearly Kähler manifold. Then \(M\) is either a 6-dimensional space of positive constant sectional curvature or locally a product of 6-dimensional strict nearly Kähler manifold of positive constant sectional curvature \(K\) and a Riemannian surface of constant Gaussian curvature \(-K\).
reviewed by: Włodzimierz Jelonek
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C55
zbMATH DE Number: 5544184
zbMATH Keywords: nearly Kähler manifold
zbMATH Keywords: Bochner flat manifold
zbMATH Keywords: conformally flat manifold
Wikidata QID: Q115357403
MaRDI profile type: Publication
full work available at URL: j.difgeo.2008.10.007
OpenAlex ID: W2040752901
cites work: Curvature and Betti Numbers. II
cites work: Bochner-Kähler metrics
cites work: Almost Hermitian surfaces with vanishing Tricerri–Vanhecke Bochner curvature tensor
cites work: Nearly Kähler manifolds
cites work: Riemannian manifolds with geodesic symmetries of order 3
cites work: The structure of nearly Kähler manifolds
cites work: The sixteen classes of almost Hermitian manifolds and their linear invariants
cites work: Q5646076
cites work: Conformally Einstein products and nearly Kähler manifolds
cites work: Nearly Kähler geometry and Riemannian foliations.
cites work: 4-dimensional conformally flat Kähler manifolds
cites work: An example of a 6-dimensional flat almost Hermitian manifold
cites work: Curvature Tensors on Almost Hermitian Manifolds
cites work: On a $K$-space of constant holomorphic sectional curvature
cites work: Q5333687
DOI: 10.1016/J.DIFGEO.2008.10.007
Recommended article: Q4709766
Recommended article: Q3790236
Recommended article: Q3327294
Recommended article: On the geometry of the Bochner tensor of nearly Kähler manifolds
Recommended article: Q3825685
Recommended article: Kählerian submersions with vanishing Bochner curvature tensor
Recommended article: Almost Hermitian Manifolds with Vanishing Bochner Curvature Tensor
Recommended article: Q3171154
Recommended article: Kähler manifolds with almost nonnegative curvature
Recommended article: Q4899793
description: scientific article; zbMATH DE number 5544184