The Globalization Problem of the Hamilton–DeDonder–Weyl Equations on a Local k-Symplectic Framework

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