In this paper, we aim at addressing the globalization problem of Hamilton–DeDonder–Weyl equations on a local k-symplectic framework and we introduce the notion of locally conformal k-symplectic (l.c.k-s.) manifolds. This formalism describes the dynamical properties of physical systems that locally behave like multi-Hamiltonian systems. Here, we describe the local Hamiltonian properties of such systems, but we also provide a global outlook by introducing the global Lee one-form approach. In particular, the dynamics will be depicted with the aid of the Hamilton–Jacobi equation, which is specifically proposed in a l.c.k-s manifold.

中文翻译：

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局部k-渐近框架上Hamilton-DeDonder-Weyl方程的全球化问题。

在本文中，我们旨在解决在局部k辛框架上的Hamilton–DeDonder–Weyl方程的全球化问题，并引入局部保形k辛（lck-s。）流形的概念。这种形式主义描述了局部行为类似于多哈密顿体系的物理系统的动力学特性。在这里，我们描述了此类系统的局部哈密顿特性，但我们也通过引入全局Lee形式方法提供了全球视野。特别是，动力学将借助在lck-s流形中特别提出的汉密尔顿-雅各比方程来描述。