Kähler contact distributions
type: Item
instance of: scholarly article
title: Kähler contact distributions
zbMATH Open document ID: 1209.53031
author: Aurel Bejancu
published in: Journal of Geometry and Physics
publication date: 2010-11-25T00:00:00Z
review text: Let \(M(\varphi ,\xi ,\eta ,g)\) be a contact metric manifold and \(\mathcal D\) be its contact distribution. We define a linear connection \(\nabla \) on \(M\) and relate it with the generalized Tanaka connection introduced by Tanno in 1989. This enables us to give a characterization in terms of \(\nabla \) of a strongly pseudo-convex \(CR\)-structure on \(M\). Then we prove that \(\nabla \varphi =0\) if and only if \(M\) is a Sasakian manifold. In this case we call \((\mathcal D, \varphi , g)\) a Kähler contact distribution. Finally, we prove that such a \((\mathcal D, \varphi , g)\) has constant holomorphic sectional curvature with respect to \(\nabla \) if and only \(M\) is a Sasakian space form.
reviewed by: Domenico Perrone
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 5819533
zbMATH Keywords: contact metric manifold
zbMATH Keywords: \(\mathcal D\)-connection
zbMATH Keywords: Kähler contact distribution
zbMATH Keywords: Sasakian manifold
zbMATH Keywords: Sasakian space form
MaRDI profile type: Publication
full work available at URL: j.geomphys.2010.04.005
OpenAlex ID: W2095345768
Wikidata QID: Q126227634
cites work: Variational Problems on Contact Riemannian Manifolds
cites work: On almost contact manifolds admitting axiom of planes or axiom of free mobility
cites work: Q3312869
cites work: Q3222791
cites work: Q5565587
DOI: 10.1016/J.GEOMPHYS.2010.04.005
description: scientific article; zbMATH DE number 5819533