Natural base-extending operators of foliations into foliations on the Weil functors
type: Item
instance of: scholarly article
title: Natural base-extending operators of foliations into foliations on the Weil functors
zbMATH Open document ID: 0837.58004
DOI: 10.1007/BF01263527
published in: Geometriae Dedicata
publication date: 1995-11-21T00:00:00Z
review text: Let \(E\) be a Weil functor with the corresponding Weil algebra \(A= E\mathbb{R}\). The author considers a \(p\)-dimensional foliation \(F\) on the differentiable manifold \(M\) and describes the construction of a canonical \(s\)-dimensional foliation \(Q(M, F)\) on the manifold \(EM\). If \((I, J)\) is a pair of ideals in \(A\) then the distribution \(Q^{(I, J)}(M, F)\) defines a foliation on \(T^A\), where \(Q^{(I, J)}(M, F)= \text{span}\{X^{(a)}: a\in I\), \(X\) is an \(F\)-vector field on \(M\}+ \text{span}\{Y^{(b)}: b\in J\), \(Y\) is a vector field on \(M\}\). Here \(X^{(a)}\) is the \((a)\)-lift of \(X\) to \(T^A M\), where \(E\) is identified with \(T^A\) -- the Weil functor of \(A\)-velocities.
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 806203
zbMATH Keywords: natural vector bundles
zbMATH Keywords: Weil functor
zbMATH Keywords: foliation
author: Włodzimierz M. Mikulski
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
cites work: Lifts of some tensor fields and connections to product preserving functors
cites work: Q3800762
cites work: On the natural operators on vector fields
cites work: Q4693714
cites work: Natural liftings of foliations to the tangent bundle
cites work: Prolongation of connections to bundles of infinitely near points
description: scientific article; zbMATH DE number 806203