Conformal Euler-Lagrangian Equations on 4-Walker Manifolds
Abstract: The main purpose of the present paper is to study almost paracomplex structures conformal Euler-Lagrangian equations on 4-dimensional Walker manifolds. A Walker nmanifold 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. In this study, 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 Euler-Lagrangian equations..
Keywords: Walker Manifolds, Holomorphic, Symplectic Geometry, Conformal Geometry, Lagrangian, Mechanical System, Riemannian Manifold, Almost Complex Manifolds.
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