Efficient construction of contact coordinates for partial prolongations

dc.creatorVassiliou, Peter J.
dc.date2004-06-11
dc.date2004-07-06
dc.date.accessioned2026-07-07T05:09:10Z
dc.date.available2026-07-07T05:09:10Z
dc.descriptionLet $\CV$ be a vector field distribution on manifold $M$. We give an efficient algorithm for the construction of local coordinates on $M$ such that $\CV$ may be locally expressed as some partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first order jet bundle of maps from $\Bbb R$ to $\Bbb R^q$, $q\geq 1$. It is proven that if $\CV$ is locally equivalent to a partial prolongation of $\Cal C^{(1)}_q$ then the explicit construction of contact coordinates algorithmically depends upon the determination of certain first integrals in a sequence of geometrically defined and algorithmically determined integrable Pfaffian systems on $M$. The number of these first integrals that must be computed satisfies a natural minimality criterion. These results therefore provide a full and constructive generalisation of the classical Goursat normal form from the theory of exterior differential systems.
dc.description23 pages
dc.identifierhttps://arxiv.org/abs/math/0406234
dc.identifierhttp://arxiv.org/abs/math/0406234
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71531
dc.subjectDifferential Geometry
dc.subject58J60; 34H05; 93B18; 93B27
dc.titleEfficient construction of contact coordinates for partial prolongations
dc.typetext

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