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Distributions admitting a local basis of homogeneous polynomials

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Castrillón López, Marco and Gadea, P.M. and Muñoz Masqué, Jaime (1999) Distributions admitting a local basis of homogeneous polynomials. Libertas Mathematica, 19 . pp. 19-27. ISSN 0278-5307

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Official URL: http://www.ara-as.org/index.php/lm/article/view/809/681




Abstract

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.


Item Type:Article
Uncontrolled Keywords:homogeneous polynomials.
Subjects:Sciences > Mathematics > Number theory
Sciences > Mathematics > Numerical analysis
ID Code:24301
Deposited On:22 Jan 2014 18:14
Last Modified:12 Dec 2018 15:13

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