Coisotropic reduction in Multisymplectic Geometry
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909424973512704 |
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| author | de León, Manuel Izquierdo-López, Rubén |
| author_facet | de León, Manuel Izquierdo-López, Rubén |
| contents | In this paper we study coisotropic reduction in multisymplectic geometry. On the one hand, we give an interpretation of Hamiltonian multivector fields as Lagrangian submanifolds and prove that $k$-coisotropic submanifolds induce a Lie subalgebra in the algebra of Hamiltonian $(k-1)$-forms, similar to how coisotropic submanifolds in symplectic geometry induce a Lie subalgebra under the Poisson bracket. On the other hand, we extend the classical result of symplectic geometry of projection of Lagrangian submanifolds in coisotropic reduction to bundles of forms, which naturally carry a multisymplectic structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_12898 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coisotropic reduction in Multisymplectic Geometry de León, Manuel Izquierdo-López, Rubén Symplectic Geometry 53D42, 70S20 In this paper we study coisotropic reduction in multisymplectic geometry. On the one hand, we give an interpretation of Hamiltonian multivector fields as Lagrangian submanifolds and prove that $k$-coisotropic submanifolds induce a Lie subalgebra in the algebra of Hamiltonian $(k-1)$-forms, similar to how coisotropic submanifolds in symplectic geometry induce a Lie subalgebra under the Poisson bracket. On the other hand, we extend the classical result of symplectic geometry of projection of Lagrangian submanifolds in coisotropic reduction to bundles of forms, which naturally carry a multisymplectic structure. |
| title | Coisotropic reduction in Multisymplectic Geometry |
| topic | Symplectic Geometry 53D42, 70S20 |
| url | https://arxiv.org/abs/2405.12898 |