arXiv subjects
Publications and source records attributed to Mehmet Tekkoyun.
In this study, we present a new analogue of Euler-Lagrange and Hamilton equations on an almost Kähler model of a Finsler manifold. Also, we give some corollories about the related mechanical systems and equations.
This study is an extented analogue to conformal geometry of the paper given by [14]. Also, the geometric and physical results related to bi-para-conformal-dynamical systems are also presented.
This manuscript presents an attempt to introduce Lagrangian formalism for mechanical systems using para-quaternionic Kahler manifolds, which represent an interesting multidisciplinary field of research. In addition to, the geometrical-physical results related to para-quaternionic Kahler mechanical systems are also given.
In the present paper, we introduce para-quaternionic Kaehler analogue of Lagrangian and Hamiltonian mechanical systems. Finally, the geometrical-physical results related to para-quaternionic Kaehler mechanical systems are also given.
This article presents the further steps of the previously done studies taking into consideration the k-th order extensions of a complex manifold. In the previous studies higher order vertical and complete lifts of structures on the complex manifold were introduced. Presently, k-th extended spaces of a product manifold have been set and the higher order vertical, complete, complete- vertical and horizontal lifts of geometric structures on the product manifold have been presented.
In this study, firstly, the k-th order extension of complex product manifold is consid- ered. Then the higher order vertical, complete lifts of geometric structures on product manifold to its extended spaces are given. Also higher order lifts of tensor field of type (1,1) are presented. And then extended contact manifolds are defined. Finally higher order vertical and complete lifts of time dependent complex Hamiltonian equations on contact manifold to its extensions are introduced. In conclusion, geometric meaning of Hamiltonian mechanical systems is discussed.
In this study, Hamiltonian and Lagrangian theories, which are mathematical models of mechanical systems, are structured on the horizontal and the vertical distributions of tangent and cotangent bundles. In the end, the geometrical and physical results related to Hamiltonian and Lagrangian dynamical systems are concluded.
The goal of this paper, using lifting theory it is to produce almost paracomplex struc- tures on the tangent bundle of almost Lorentzian r-paracontact manifold endowed with almost Lorentzian r-paracontact structure. Finally, we discuss the effect over dynamics systems of the produced geometrical structures.
In this study, we introduce Euler-Lagrange and Hamiltonian equations on (R2; g; J) being a model of para-Kaehlerian Space Forms. Finally, some geometrical and physical results on the related mechanic systems have been discussed.
In this study, Clifford Kaehler analogue of Lagrangian dynamics is introduced. Also,the some geometrical and physical results over the obtained Clifford Kaehler dynamical systems are discussed.
This paper presents Hamilton dynamics on Clifford Kaeler manifolds. In the end, the some results related to Clifford Kaehler dynamical systems are also discussed.
The aim of this study is to introduce quaterinon Kaehler analogue of Lagrangian mechanics. Finally, the geometric and physical results related to quaternion Kaehler dynamical systems are also presented.
In this study, it is introduced paracomplex analogue of Lagrangians and Hamiltonians with constraints in the framework of para-Kaehlerian manifolds. The geometrical and mechanical results on the constrained mechanical system have also been discussed.
In this study, taking into considering lifting theory, we shall obtain both almost complex and paracomplex structures on the tangent bun- dle, based on almost Lorentzian r-contact and r-paracontact manifold.
In this study, it is generalized the concept of Lagrangian mechanics with constraints to complex case. To be beginning, it is considered a Kaehlerian manifold as a velocity-phase space. Then a non-holonomic constraint is given by 1-form on it. If the form is closed, it is found that the constraint is (locally) holonomic. In the result, complex analogous of some topics in constrained Lagrangian mechanical system is concluded.
The goal of this paper is to introduce the lifting theory that has an important role in geometry. Therefore, using the lifts of differential geometric structures we show that tangent bundle TM of paracomplex manifold M admits para-complex torsion-free affine connection.
In this paper, Lagrangian formalisms of Classical Mechanics was deduced on Kaehlerian manifold being geometric model of a generalized Lagrange space.Then, it was given two applications of complex Euler-Lagrange equations on mechanics system.
This study introduces standard Cliffordian Kaehler analogue of Hamiltonian mechanic systems. In the end, the some results related to standard Cliffordian Kaehler dynamical systems are also discussed.