A note on almost Kähler and nearly Kähler submersions
type: Item
instance of: scholarly article
title: A note on almost Kähler and nearly Kähler submersions
zbMATH Open document ID: 0967.53023
DOI: 10.1007/BF01237477
author: Maria Falcitelli
author: Anna Maria Pastore
published in: Journal of Geometry
publication date: 2001-09-03T00:00:00Z
review text: Let \((M,g,J)\) and \((B,g',J')\) be almost Hermitian manifolds. A Riemannian submersion \(\pi:M\to B\) is called an almost Hermitian submersion if \(\pi_*J= J'\pi_*\). An almost Hermitian submersion is called a nearly Kähler or an almost Kähler submersion if the total space is nearly Kähler or almost Kähler, respectively. The aim of this paper is to study the curvature of the total space, of the fibres and of the base manifold of such submersions. Further, the authors prove: If \(\pi\) is a nearly Kähler (almost Kähler) submersion, then the horizontal distribution of \(\pi\) is integrable and totally geodesic.
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 53C40
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 1565895
zbMATH Keywords: Riemannian curvature
zbMATH Keywords: integrability
zbMATH Keywords: almost Hermitian manifolds
zbMATH Keywords: Riemannian submersion
zbMATH Keywords: almost Hermitian submersion
zbMATH Keywords: horizontal distribution
reviewed by: Costache Apreutesei
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01237477
OpenAlex ID: W2913905320
description: scientific article; zbMATH DE number 1565895