dc.contributor
Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor
Universitat Politècnica de Catalunya. GEOMVAP - Geometria de Varietats i Aplicacions
dc.contributor.author
Gràcia Sabaté, Francesc Xavier
dc.contributor.author
Rivas Guijarro, Xavier
dc.contributor.author
de Lucas Araujo, Javier
dc.contributor.author
Román Roy, Narciso
dc.date.issued
2023-06-14
dc.identifier
Gràcia, X. [et al.]. On Darboux theorems for geometric structures induced by closed forms. 2023.
dc.identifier
https://arxiv.org/abs/2306.08556
dc.identifier
https://hdl.handle.net/2117/427695
dc.description.abstract
This work reviews the classical Darboux theorem for symplectic, presymplectic, and cosymplectic manifolds (which are used to describe regular and singular mechanical systems), and certain cases of multisymplectic manifolds, and extends it in new ways to k-symplectic and k-cosymplectic manifolds (all these structures appear in the geometric formulation of first-order classical field theories). Moreover, we discuss the existence of Darboux theorems for classes of precosymplectic, k-presymplectic, k-precosymplectic, and premultisymplectic manifolds, which are the geometrical structures underlying some kinds of singular field theories. Approaches to Darboux theorems based on flat connections associated with geometric structures are given, while new results on polarisations for (k-)(pre)(co)symplectic structures arise.
dc.description.abstract
Preprint
dc.format
application/pdf
dc.subject
Àrees temàtiques de la UPC::Matemàtiques i estadística
dc.subject
Darboux theorem
dc.subject
Flat connection
dc.subject
k-cosymplectic manifold
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k-precosymplectic manifold
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k-presymplectic manifold
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k-symplectic manifold
dc.subject
Multisymplectic manifold
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Premultisymplectic manifold
dc.title
On Darboux theorems for geometric structures induced by closed forms
dc.type
External research report
