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Conformal Weyl-Euler-Lagrangian Equations on 4-Walker Manifolds

Journal: NEW TRENDS IN MATHEMATICAL SCIENCES (Vol.4, No. 2)

Publication Date:

Authors : ;

Page : 11-22

Keywords : Walker Manifolds Weyl Theory holomorphic symplectic geometry conformal geometry Lagrangian mechanical system Riemannian manifold almost complex manifolds.;

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Abstract

The main purpose of the present paper is to study almost complex structures conformal Weyl-Euler-Lagrangian equations on 4-dimensional Walker manifolds for (conservative) dynamical systems. In this study, routes of objects moving in space will be modeled mathematically on 4-dimensional 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.

Last modified: 2016-10-30 05:09:52