Nearly Kähler and Hermitian \(f\)-structures on homogeneous \(k\)-symmetric spaces
type: Item
instance of: scholarly article
title: Nearly Kähler and Hermitian \(f\)-structures on homogeneous \(k\)-symmetric spaces
zbMATH Open document ID: 1209.53021
DOI: 10.1134/S1064562410030130
author: Vitaly V. Balashchenko
author: A. S. Samsonov
published in: Doklady Mathematics
publication date: 2010-12-08T00:00:00Z
review text: The aim of this paper is to show that all the base canonical \(f\)-structures on naturally reductive \(k\)-symmetric spaces (where \(k\geq 3\)) are nearly Kähler \(f\)-structures. The authors give a criterion for a canonical \(f\)-structure to be the sum or difference of two base \(f\)-structures to be nearly Kähler. They describe those base \(f\)-structures which are also Hermitian and they give a criterion for the remaining base structures to be Hermitian. The paper is very short. It contains the basic definitions and main results. The proofs are not completely worked out but only sketched.
reviewed by: Gabriela Paola Ovando
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 53D15
zbMATH DE Number: 5824793
zbMATH Keywords: \(f\)-structures
zbMATH Keywords: nearly Kähler
zbMATH Keywords: Hermitian
zbMATH Keywords: \(k\)-symmetric spaces
MaRDI profile type: Publication
cites work: Homogeneous spaces defined by Lie group automorphisms. I
cites work: Riemannian manifolds with geodesic symmetries of order 3
cites work: Generalized symmetric spaces
full work available at URL: s1064562410030130
OpenAlex ID: W2025987675
description: scientific article; zbMATH DE number 5824793