Homogeneous structures on manifolds: Differential geometry from the point of view of differential equations
type: Item
instance of: scholarly article
title: Homogeneous structures on manifolds: Differential geometry from the point of view of differential equations
zbMATH Open document ID: 0801.58043
DOI: 10.1007/BF01250547
published in: Mathematical Notes
publication date: 1994-02-08T00:00:00Z
review text: Let \(N\) be a manifold together with a transitive action of the Lie group \(G\) and \(M\) be any smooth manifold with \(\dim M= \dim N\). The author calls a free \((N,G)\)-coframe of order \(k\) at a point \(x\in M\) the \(k\)-jet of a local diffeomorphism \(\varphi: M\to N\) at this point and denotes by \(R^ k (M)\) the space of all free \(k\)-coframes. The Lie group \(G\) acts in a natural way in the fiber bundle of free coframes. By a homogeneous \((N,G)\)-structure on a manifold \(M\) he means a subbundle \(E_ k\subset R^ k(M)\) which is the principal \(G\)-bundle with respect to the action of the group \(G\) in the space \(R^ k(M)\). In the paper under review, the author considers some properties of such structures related to systems of differential equations, Cartan connection and its curvature.
Mathematics Subject Classification ID: 58H15
Mathematics Subject Classification ID: 53C15
Mathematics Subject Classification ID: 58-02
zbMATH DE Number: 484282
zbMATH Keywords: symbol of the system of differential equations
zbMATH Keywords: Cartan distribution
zbMATH Keywords: Cartan connection
zbMATH Keywords: Bott connection
Wikidata QID: Q115393780
author: Valentin Lychagin
reviewed by: Witold Mozgawa
MaRDI profile type: Publication
cites work: Integrability criteria for systems of nonlinear partial differential equations
cites work: Overdetermined systems of linear partial differential equations
cites work: CONTACT GEOMETRY AND NON-LINEAR SECOND-ORDER DIFFERENTIAL EQUATIONS
cites work: Lie Equations, Vol. I
description: scientific article; zbMATH DE number 484282