Some Properties of Multisymplectic Manifolds

Román‐Roy, Narciso

doi:10.1007/978-3-030-24748-5_18

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2023

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Cited by 2 publications

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References 27 publications

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“…Multisymplectic structures [7,14,17,26,30], higher Poisson structures [6,23], pre-multisymplectic structures and Nambu-Poisson structures [16,21,31] which play important roles in mathematical physics. It is natural how to construct them via some foliation from Dirac structures.…”

Section: Introductionmentioning

confidence: 99%

Weak $(p,k)$-Dirac manifolds

Bi¹,

Chen²

2023

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In this paper, we introduce the notion of a weak (p, k)-Dirac structure in T M ⊕ Λ p T * M , where 0 ≤ k ≤ p − 1. The weak (p, k)-Lagrangian condition has more informations than the (p, k)-Lagrangian condition and contains the (p, k)-Lagrangian condition. The weak (p, 0)-Dirac structures are exactly the higher Dirac structures of order p introduced by N. Martinez Alba and H. Bursztyn in [23] and [6], respectively. The regular weak (p, p − 1)-Dirac structure together with (p, p − 1)-Lagrangian subspace at each point m ∈ M have the multisymplectic foliation. Finally, we introduce the notion of weak (p, k)-Dirac morphism. We give the condition that a weak (p, k)-Dirac manifold is also a weak (p, k)-Dirac manifold by pulling back.

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