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

Year 2016, Volume: 4 Issue: 2, 11 - 22, 01.03.2016

Zeki Kasap

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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