魏尔束上的交映结构与应用

Pub Date : 2024-01-29 DOI:10.1007/s13370-024-01166-9

Andre S. E. Mialebama Bouesso, F. Mekiya Moutabanza, Jude R. Bayeni Mitoueni

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引用次数: 0

摘要

让 M 是光滑流形，A 是魏尔代数。我们介绍并讨论了 Weil 束 \((M^A,\pi ,M)\) 中的交映结构，并建立了 M 中的交映结构与 \(M^A.\) 中的交映结构之间的联系。作为应用，我们讨论了这两种情况下的哈密顿向量场、交映向量场和泊松结构。

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Symplectic structure and applications on Weil bundles

Let M be a smooth manifold and A a Weil algebra. We introduce and discuss the symplectic structure in the Weil bundle \((M^A,\pi ,M)\) and we establish the link between the symplectic structure in M and that in \(M^A.\) As applications, we discuss Hamiltonian vector fields, symplectic vector fields and poisson structures in both cases.

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