Some applications of the Mangiarotti-Modugno formula for tangent-valued forms
type: Item
instance of: scholarly article
zbMATH Open document ID: 1307.58001
DOI: 10.1142/S0219887814600226
published in: International Journal of Geometric Methods in Modern Physics
publication date: 2014-10-20T00:00:00Z
Mathematics Subject Classification ID: 58A32
Mathematics Subject Classification ID: 53C05
zbMATH DE Number: 6359101
zbMATH Keywords: general connection
zbMATH Keywords: vertical prolongation of connections
zbMATH Keywords: Frölicher-Nijenhuis bracket
zbMATH Keywords: Weil bundle
zbMATH Keywords: torsion
MaRDI profile type: Publication
cites work: Weil bundles as generalized jet spaces
cites work: Torsions of connections on some natural bundles
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author: Ivan Kolář
title: Some applications of the Mangiarotti-Modugno formula for tangent-valued forms
review text: The author presents a classical approach to a general connection on an arbitrary fibered manifold \(Y\to M\). He presents the covariant approach to the Weil bundle for every Weil algebra \(A\), that generalizes the concept of \((k,r)\)-velocity introduced by Ehresmann. He introduces the concept of a-torsion of an arbitrary tangent-valued form on a Weil bundle \(T^{A}M\), for any \(a\in A\). Applying the graded Jacobi identity, he proves a far-going generalization of a first Bianchi identity for classical connections in terms of a Frölicher-Nijenhuis bracket and he deduces two results concerning \(f\)-relatedness, for a differentiable map \(f:M\to N\), which clarifies a remarkable functorial character of a-torsion.
reviewed by: Basile Guy Richard Bossoto
description: scientific article; zbMATH DE number 6359101