Weyl-Mechanical Systems on Generalized (Para)-Kähler Space Form

Abstract

Euler-Lagrange and Hamilton equations on Kähler-Weyl manifolds were presented and the para-complex mathematical aspects of Lagrangian and Hamilton operator, dynamic equation, the action functional, Lagrangian and Hamilton's principle and equations and so on were given. The most important result revealed by this study, how to find the Lagrangian and Hamiltonian equations of motion without using the dynamic equations. For this, theorems were used as an alternative method of finding equations. As a result of this study, Weyl-Euler-Lagrange and Weyl-Hamilton partial differential equations were obtained for movement of objects on Kähler-Weyl manifolds.