arXiv subjects

Nejat Ekmekci

Publications and source records attributed to Nejat Ekmekci.

4 recordsLinked to original sources

arXiv2017

Algebraic properties of bi$-$periodic dual Fibonacci quaternions

The purpose of the paper is to construct a new representation of dual quaternions called bi$-$periodic dual Fibonacci quaternions. These quaternions are originated as a generalization of the known quaternions in literature such as dual Fibonacci quaternions, dual Pell quaternions and dual $k-$Fibonacci quaternions. Furthermore, some of them have not been introduced until this time. Then, we give generating function, Binet formula and Catalan's identity in terms of these quaternions.

math.GM↗

arXiv2014

On The Special Curves In Minkowski 4 Spacetime

In [1], we gave a method for constructing Bertrand curves from the spherical curves in 3 dimensional Minkowski space. In this work, we construct the Bertrand curves corresponding to a spacelike geodesic and a null helix in Minkowski 4 spacetime.

math.DG↗

arXiv2012

On Mannheim Partner Curves in three Dimensional Lie Groups

In this paper, we define Mannheim partner curves in a three dimensional Lie group G with a bi-invariant metric. And then the main result in this paper is given as (Theorem 3.3): A curve α with the Frenet apparatus {T,N,B,κ,τ} in G is a Mannheim partner curve if and only if λκ(1+H2)=1, where λ is constant and H is the harmonic curvature function of the curve α.

math.DG↗

arXiv2012

Bertrand Curves in three Dimensional Lie Groups

In this paper, we give the defination of harmonic curvature function some special curves such as helix, slant curves, Mannheim curves and Bertrand curves. Then, we recall the characterizations of helices [8], slant curves (see [19]) and Mannheim curves (see [12]) in three dimensional Lie groups using their harmonic curvature function. Moreover, we define Bertrand curves in a three dimensional Lie group G with a bi-invariant metric and the main result in this paper is given as (Theorem 3.4): A curve ?α with the Frenet apparatus {T,N,B,κ,τ} in G is a Bertrand curve if and only if λκ+μκH=1 where λ,μ ? are constants and H is the harmonic curvature function of the curve α.

math.DG↗