The trace decomposition problem
type: Item
instance of: scholarly article
title: The trace decomposition problem
zbMATH Open document ID: 0839.15024
published in: Beiträge zur Algebra und Geometrie
publication date: 1996-06-04T00:00:00Z
full work available at URL: https://eudml.org/doc/223759
full work available at URL: no.2
review text: The trace decomposition problem is considered, i.e. the problem of existence and uniqueness of a decomposition of a tensor in which one term is traceless and the remaining terms form a linear combination of Kronecker's \(\delta\)-tensor with traceless coefficients. Two basic theorems are given which provide a complete solution of the trace decomposition problem. In the particular cases of the tensor spaces of type (1, 2), (1, 3) and (2, 2) explicit decomposition formulas are given. These formulas are applied to the torsion and curvature tensors on a manifold endowed with a linear connection or a metric. It is shown that the trace decompositions lead to the Weyl projective and conformal curvature tensors.
Mathematics Subject Classification ID: 15A72
Mathematics Subject Classification ID: 53A55
zbMATH DE Number: 821698
zbMATH Keywords: traceless tensor
zbMATH Keywords: trace decomposition problem
zbMATH Keywords: tensor spaces
zbMATH Keywords: torsion and curvature tensors
zbMATH Keywords: Weyl projective and conformal curvature tensors
author: Demeter Krupka
reviewed by: Valeriu Prepeliţă
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 821698