Weyl-Mechanical Systems on Tangent Manifolds of Constant W-Sectional Curvature

Kasap, Zeki

doi:10.1142/s0219887813500539

Cited by 4 publications

(2 citation statements)

References 16 publications

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“…Kasap and Tekkoyun [18] obtained Lagrangian and Hamiltonian formalism for mechanical systems using para/pseudo-Kähler manifolds, representing an interesting multidisciplinary field of research. Kasap [19] introduced that the Weyl-Euler-Lagrange and Weyl-Hamilton equations on , 2n n R which is a model of tangent manifolds of constant W-sectional curvature. Tekkoyun [20] found paracomplex analogue of Euler-Lagrange and Hamiltonian equations.…”

Section: Introductionmentioning

confidence: 99%

Euler-Lagrange Equations With 3-Dimensional Real Number Space on an Almost Paracontact Manifold

2016

Jour. Pure Appl. Math. Adv. Appl.

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We consider Euler-Lagrange equations on almost paracontact manifolds. It is well known that the geometry of almost contact manifolds is a natural extension in the odd dimensional case of almost Hermitian geometry. A Hermitian manifold is a complex manifold with a Hermitian metric on its holomorphic tangent space. Also, the contact geometry as symplectic geometry has large and comprehensive applications in physics, geometrical optics, classical mechanics, thermodynamics, geometric quantization, and applied mathematics. On the other hand, one way of solving problems in classical and analytical mechanics is through use of the Euler-Lagrange equations. The purpose of the present paper is to solve the problems of classical mechanics with 3-dimensional real number space on an almost paracontact manifold by using Euler-Lagrange equations.

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Section: Introductionmentioning

confidence: 99%

Euler-Lagrange Equations With 3-Dimensional Real Number Space on an Almost Paracontact Manifold

2016

Jour. Pure Appl. Math. Adv. Appl.

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“…Kasap and Tekkoyun investigated Lagrangian and Hamiltonian formalism for mechanical systems using para-/pseudo-Kähler manifolds, representing an interesting multidisciplinary field of research [4]. Kasap obtained the Weyl-Euler-Lagrange and the Weyl-Hamilton equations on R 2 which is a model of tangent manifolds of constantsectional curvature [5]. Kapovich demonstrated an existence theorem for flat conformal structures on finite-sheeted coverings over a wide class of Haken manifolds [6].…”

Section: Introductionmentioning

confidence: 99%

Weyl-Euler-Lagrange Equations of Motion on Flat Manifold

Kasap

2015

Advances in Mathematical Physics

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This paper deals with Weyl-Euler-Lagrange equations of motion on flat manifold. It is well known that a Riemannian manifold is said to be flat if its curvature is everywhere zero. Furthermore, a flat manifold is one Euclidean space in terms of distances. Weyl introduced a metric with a conformal transformation for unified theory in 1918. Classical mechanics is one of the major subfields of mechanics. Also, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange equations. In this study, partial differential equations have been obtained for movement of objects in space and solutions of these equations have been generated by using the symbolic Algebra software. Additionally, the improvements, obtained in this study, will be presented.

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Dynamics Equations with Almost Complex Structures on Contact 5-Manifolds

Kasap¹

2014

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Weyl-Mechanical Systems on Tangent Manifolds of Constant W-Sectional Curvature

Cited by 4 publications

References 16 publications

Euler-Lagrange Equations With 3-Dimensional Real Number Space on an Almost Paracontact Manifold

Euler-Lagrange Equations With 3-Dimensional Real Number Space on an Almost Paracontact Manifold

Weyl-Euler-Lagrange Equations of Motion on Flat Manifold

Dynamics Equations with Almost Complex Structures on Contact 5-Manifolds

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