Natural base-extending operators of foliations into foliations on the Weil functors
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.
scientific article; zbMATH DE number 806203