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arXiv · 2410.15507

Coisotropic embeddings of precosymplectic manifolds

Manuel de León·Pablo Soto Martín
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Abstract

In this paper we provide a complete characterisation of coisotropic embeddings of precosymplectic manifolds into cosymplectic manifolds. This result extends a theorem of Gotay about coisotropic embeddings of presymplectic manifolds. We also extend to the cosymplectic case some results of A. Weinstein which generalise the Darboux theorem. While symplectic geometry is the natural framework for developing Hamiltonian mechanics, cosymplectic geometry is the corresponding framework for time-dependent Hamiltonian mechanics. The motivation behind proving this theorem is to generalise known results for symplectic geometry to cosymplectic geometry, so that they can be used to study time-dependent systems, for instance for the regularization problem of singular Lagrangian systems.

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Manuel de León, Pablo Soto Martín. 2024-10-20. Coisotropic embeddings of precosymplectic manifolds. https://arxiv.org/abs/2410.15507

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