A constructive generalised Goursat normal form

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dc.creatorVassiliou, Peter J.
dc.date2004-04-21
dc.date.accessioned2026-07-07T05:07:36Z
dc.date.available2026-07-07T05:07:36Z
dc.descriptionWe provide necessary and sufficient conditions on the derived type of a vector field distribution $\Cal V$ in order that it be locally equivalent to a partial prolongation of the contact distribution $\Cal C^{(1)}_q$, on the first order jet bundle of maps from $\Bbb R$ to $\Bbb R^q$, $q\geq 1$. This result fully generalises the classical Goursat normal form. Our proof is constructive: it is proven that if $\Cal V$ is locally equivalent to a partial prolongation of $\Cal C^{(1)}_q$ then the explicit construction of contact coordinates algorithmically depends upon the integration of a sequence of geometrically defined and algorithmically determined integrable Pfaffian systems on the ambient manifold.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math/0404377
dc.identifierhttp://arxiv.org/abs/math/0404377
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/70921
dc.subjectDifferential Geometry
dc.subject58J60
dc.titleA constructive generalised Goursat normal form
dc.typetext

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