%0 Journal Article
%A Castrillón López, Marco
%A Gadea, P.M.
%A Muñoz Masqué, Jaime
%T Distributions admitting a local basis of homogeneous polynomials
%D 1999
%@ 0278-5307
%U https://hdl.handle.net/20.500.14352/58909
%X The paper is a survey of several results by the authors, the main one of them being the following characterization of homogeneous algebraic distributions: Let us consider a vertical distribution D on the vector bundle p:E→M locally spanned by vertical vector fields X1,⋯,Xr. Let χ be the Liouville vector field of the vector bundle. Then there exists an r×r invertible matrix with smooth entries (cij) such that the vector fields Yj=∑ri=1cijXi, 1≤j≤r, are homogeneous algebraic of degree d if and only if there exists an r×r matrix A=(aij) of smooth functions given by [χ,Xj]=∑ri=1aijXi such that A restricted to the zero section of E is(d−1) times the identity matrix.    Examples and applications are given.
%~