Conformal Weyl-Euler-Lagrangian equations on 4-Walker manifolds

Abstract

The main purpose of the present paper is to study almost complex structures conformalWeyl-Euler-Lagrangian equations on 4-imensionalWalker manifolds for (conservative) dynamical systems. In this study, routes of objects moving in space will be modeled mathematically on 4-imensional Walker manifolds that these are time-dependent partial differential equations. A Walker n-manifold is a semi-Riemannian n-manifold, which admits a field of parallel null r-planes, with r <= n/2 . It is well-known that semi-Riemannian geometry has an important tool to describe spacetime events. Therefore, solutions of some structures about 4-Walker manifold can be used to explain spacetime singularities. Then, here we present complex analogues of Lagrangian mechanical systems on 4-Walker manifold. Also, the geometrical-physical results related to complex mechanical systems are also discussed for conformal Weyl-Euler-Lagrangian equations for (conservative) dynamical systems and solution of the motion equations using Maple Algebra software will be made.

Keywords

• Walker Manifolds,Weyl theory,holomorphic,symplectic geometry,conformal geometry,Lagrangian,mechanical system,Riemannian manifold

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