Mechanical Systems on Almost Para/Pseudo-Kähler–Weyl Manifolds (original) (raw)
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Hamilton Equation on Almost Pseudo Kähler-Weyl Manifolds for Mechanical Systems
International Journal of Applied Mathematics and Machine Learning, 2015
This paper aims to present Hamiltonian formalism for mechanical systems using pseudo-Kähler Weyl manifolds, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations will be made by using the Maple computer program. In this study, some geometrical, relativistic, mechanical, and physical results related to pseudo-Kähler Weyl mechanical systems are also given.
This paper aims to present Hamiltonian formalism for mechanical systems using pseudo-Kähler Weyl manifolds, which represent an interesting multidisciplinary field of research. As a result of this study, partial differential equations will be obtained for movement of objects in space and solutions of these equations will be made by using the Maple computer program. In this study, some geometrical, relativistic, mechanical, and physical results related to pseudo-Kähler Weyl mechanical systems are also given.
Weyl-Mechanical Systems on Generalized (Para)-Kähler Space Form
Journal of Pure and Applied Mathematics: Advances and Applications, 2020
Euler-Lagrange and Hamilton equations on Kähler-Weyl manifolds were presented and the para-complex mathematical aspects of Lagrangian and Hamilton operator, dynamic equation, the action functional, Lagrangian and Hamilton's principle and equations and so on were given. The most important result revealed by this study, how to find the Lagrangian and Hamiltonian equations of motion without using the dynamic equations. For this, theorems were used as an alternative method of finding equations. As a result of this study, Weyl-Euler-Lagrange and Weyl-Hamilton partial differential equations were obtained for movement of objects on Kähler-Weyl manifolds.
Differential geometry and mathematical physics deal with metrical notions on manifolds that it began as the study of curves and surfaces using the methods of calculus. The most important class of Hermitian manifolds are Kähler manifolds. An almost Hermitian manifold whose associated (1,1)-form is closed is naturally called an almost Kähler manifold. A geodesic is the shortest route between two points on the Earth's surface and it is called as a curve. A geodesic is a generalization of the notion of a straight line to curved spaces at differential geometry. Classical mechanics has a large working area on geodesics. On the other hand, one way of solving problems in classical mechanics occurs with the help of the Euler-Lagrange and the Hamilton equations. In this study, we obtained dynamics equations by using the Euler-Lagrange and the Hamilton mechanical equations as a representive of the object motion on an almost Kähler manifolds for geodesics. Also, implicit solutions of the differential equations found in this study are solved by Maple computation program and the geodesic graphs are drawn.
28. ARTICLE: Hamiltonian Equations of Kähler-Einstein Manifolds with Equal Kähler Angles
The paper aims to introduce Hamiltonian formalism for mechanical systems using Kähler-Einstein manifolds with equal Kähler angles, which represent an interesting multidisciplinary field of research. Also, solutions of these equations will be made using the computer program Maple and the geometrical-physical results related to on Kähler-Einstein mechanical systems are also to be issued.
Hamiltonian Equations of Kähler-Einstein Manifolds with Equal Kähler Angles
The paper aims to introduce Hamiltonian formalism for mechanical systems using Kähler-Einstein manifolds with equal Kähler angles, which represent an interesting multidisciplinary field of research. Also, solutions of these equations will be made using the computer program Maple and the geometrical-physical results related to on Kähler-Einstein mechanical systems are also to be issued.
Hamiltonian Equations On Kähler-Einstein Fano- Weyl Manifolds
The paper aims to introduce Hamiltonian equations for mechanical systems using Kä hler angles on Kä hler-Einstein Fano-Weyl manifold which represent an interesting multidisciplinary field of research. Also, solutions of these equations will be made using the computer program with Maple and the geometrical-physical results related to on Kä hler-Einstein Fano-Weyl mechanical systems are also to be issued.