On a problem of Chern-Akivis-Shelekhov on hexagonal three-webs
type: Item
instance of: scholarly article
title: On a problem of Chern-Akivis-Shelekhov on hexagonal three-webs
zbMATH Open document ID: 0845.53011
DOI: 10.1007/BF01831136
published in: Aequationes Mathematicae
publication date: 1996-09-11T00:00:00Z
full work available at URL: https://eudml.org/doc/137626
review text: As is proved in [the reviewer, J. Sov. Math. 44, No. 2, 153-190 (1989; Zbl 0711.53013)], any multidimensional hexagonal 3-web \(W\) has the 4th-order closed structure (in the sense of M. A. Akivis), that is the second-order (covariant) derivatives of the curvature tensor \(b\) of \(W\) can be expressed in terms of the tensors \(a\) (torsion), \(b\) and the first-order derivatives of \(b\). In the paper under review, the corresponding relations are found in an explicit form. To obtain these relations, the author rewrites the structure equations of a hexagonal 3-web in a more laconic and convenient form. As a result, all 4th-order tensors can be expressed in terms of only one of them.
Mathematics Subject Classification ID: 53A60
Mathematics Subject Classification ID: 20N05
zbMATH DE Number: 856821
zbMATH Keywords: multidimensional three-web
zbMATH Keywords: hexagonal web
zbMATH Keywords: structure equations
author: Pavel O. Mikheev
reviewed by: A. M. Shelekhov
MaRDI profile type: Publication
cites work: Topologische Fragen der Differentialgeometrie. LXII. Eine Invariantentheorie der Dreigewebe aus \(r\)-dimensionalen Mannigfaltigkeiten im \(\mathbb{R}_{2r}\)
cites work: Q3715784
cites work: Q3972229
cites work: The g-structure associated with a multidimensional hexagonal 3-web, is closed
cites work: Web geometry
cites work: Q3980688
OpenAlex ID: W2039204006
description: scientific article; zbMATH DE number 856821