# Yılmaz TunçerUsak Üniversitesi · Department of Mathematics

Yılmaz Tunçer

Professor

## About

52

Publications

3,833

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120

Citations

Citations since 2016

Introduction

Additional affiliations

September 1996 - September 2015

September 1996 - October 2015

## Publications

Publications (52)

In the present study, we determined quantum entanglement in a full trapped ion (TRI)-coherent system and its dependence on the LambDicke parameter (LDP). We investigated the entanglement in view of two elaborated measurements of the family: entropy and fidelity. We selected three values of the deep LDP to demonstrate the benefits of these two criti...

In this study, we define tubular surfaces in Pseudo Galilean 3-space as type-1 or type-2. Using the X(s, t) position vectors of the surfaces and G(s, t) Gaussian transformations , we obtain equations for the two types of tubular surfaces that satisfy the conditions ∆X(s, t) = 0, ∆X(s, t) = AX(s, t), ∆X(s, t) = λX(s, t), ∆X(s, t) = ∆G(s, t), ∆G(s, t...

In this study, we define the X -torque curves, $$X-$$ X - equilibrium curves, X -moment conservative curves, $$X-$$ X - gyroscopic curves as new curves derived from a regular space curve by using the Frenet vectors of a space curve and its position vector, where $$X\in \left\{ T\left( s\right) , N\left( s\right) , B\left( s\right) \right\} $$ X ∈ T...

In a set of points that corresponds a vector of vector space constructed on a field is called an affine space associate with vector space. We denote as affine 3-space associated with. The first written sources that can be achieved about affine space curve theory are based on the 1890's when Ernesto Ces\`{a}ro and Die Schon von Pirondini lived perio...

In this study, we investigated the natural mates of equiaffine curves with constant equiaffine curvatures, associated to equiaffine frame in affine 3-space and we gave the position vectors under some conditions.

In this paper, we study spherical images of the modified orthogonal vector fields and Darboux vector of a regular curve which lies on the unit sphere in Euclidean 3-space.

In this paper, we defined the admissible canal surfaces with isotropic radious vector in Galilean 3-spaces an we obtained their position vectors. Also we gave some important results by using their Gauss and mean curvatures.

In this study, we gave an alternative kinematic model for two smooth submanifolds M and N both on another and inside of another, along given any two curves which are tangent to each other on M and N at every moment , which the motion accepted that these curves are trajectories of the instantaneous rotation centers at the contact points of these sub...

In this paper, we investigate the properties of curves of constant breadth in a 3-dimensional Lie group. Also, we find the condition of general helix as constant breadth curves and construct constant breadth curves which the tangent component of the curve vanishes.

In this study, we introduced the vectorial moments as a new curves as (Formula presented.)-dual curve, where (Formula presented.), constructed by the Frenet vectors of a regular curve in Euclidean 3-space and we gave the Frenet apparatus of (Formula presented.)-dual curves and also we applied to helices and curve pairs of constant breadth.

In this study, we investigated the (K,H),(K,KII ), (H,KII )-Weingarten and
(K,H),(K,KII ),(H,KII ) and (K,H,KII )-linear Weingarten canal surfaces in
IR3.

In this study we have defined Bäcklund transformations of curves according to Bishop frame preserving the natural curvatures under certain assumptions in Minkowski 3-space.

In this study, non-null Frenet-Mannheim curves and non-null Weakened Mannheim curves are investigated in Minkowski 3-space. Some characterizations for this curves are obtained.

In this study, we examined the ruled surfaces in Euclidean 3-space with the
Bishop frame of the base curve in two cases and obtained some characteri-
zations on the ruled surfaces by using its directrix, Bishop curvatures, shape
operator and Gauss curvature. Furthermore, we calculated Bishop Steiner rota-
tion, Bishop tranlation vectors, the pitch...

In this paper, we studied the timelike and the spacelike ruled surfaces in
Minkowski 3-space by using the angle between unit normal vector of the ruled surface and
the principal normal vector of the base curve. We obtained some characterizations on the
ruled surfaces by using its rulings, the curvatures of the base curve, the shape operator and
Gau...

In this study, we obtained an equation of homothetic motion of any regular surface M on its tangent plane at the contact points, along pole curves which are trajectories of instantaneous rotation centers and we gave some remarks for the homothetic motions will be both sliding and rolling at every moments. In addition, we establish a suprising relat...

In this study, we examined the ruled surfaces in Euclidean 3-space with different way. We obtained some characterizations on the ruled surfaces by using its rulings, curvatures of the base curve, shape operator and Gauss curvature.

We study quadric surfaces in Euclidean 3-space with non-degenerate second fundamental form, and classify them in terms of the Gaussian curvature, the mean curvature, the second Gaussian curvature and the second mean curvature.

In this paper, we have defined canal surfaces in Galilean and Pseudo-Galilean 3-spaces.Then, we have studied Tubular surface in Galilean and Pseudo-Galilean 3-space satisfying some equations in terms of the Gaussian curvature and the mean curvature.We have discussed Weingarten, linear Weingarten conditions and HK−quadric type for this surface with...

In this paper, we define a generalized Mannheim quaternionic curve in the four-dimensional Euclidean space R4 and investigate the properties of it.

In this work, we studied the properties of the spherical indicatrices of a Bertrand curve and its mate curve and presented some characteristic properties in the cases that Bertrand curve and its mate curve are slant helices, spherical indicatrices are slant helices and we also researched that whether the spherical indicatrices made new curve pairs...

In this study, non-null Frenet-Mannheim curves and non-null Weakened Mannheim
curves are investigated in Minkowski 3-space. Some characterizations for this
curves are obtained.

In this work, we studied the properties of the spherical indicatrices of
involute curve of a space curve and presented some characteristic properties in
the cases that involute curve and evolute curve are slant helices and helices,
spherical indicatrices are slant helices and helices and we introduced new
representations of spherical indicatrices.

In this study, Frenet-Mannheim curves and Weakened Mannheim
curves are investigated in Galilean 3-space. Some characterizations for this
curves are obtained.

In this study, we investigated the (K,H), (K,K_{II}), (H,K_{II})-Weingarten
and (K,H),(K,K_{II}),(H,K_{II}) and (K,H,K_{II})-linear Weingarten canal
surfaces in IR^3.

In this study, we analyze the general canal surfaces in terms of the features
flat, II-flat minimality and II-minimality, namely we study under which
conditions the first and second Gauss and mean curvature vanishes, i.e. K=0,
H=0, K_{II}=0 and H_{II} =0. We give a non-existence result for general canal
surfaces in E^3 with vanishing the curvatures...

In this paper, we investigate special Smarandache curves according to Bishop
frame in Euclidean 3-space and we give some differential geometric properties
of Smarandache curves. Also we find the centers of the osculating spheres and
curvature spheres of Smarandache curves.

In this paper, we study a tubular surfaces with Bishop frame in Euclidean 3-space satisfying some equations in terms of the Gaussian curvature, the mean curvature,the second Gaussian curvature and second mean curvature.

We also introduce forward curvature of a curve and give some formulas to
calculate forward curvature of a curve on time scales which may be an arbitrary
closed subsets of the set of all real numbers. We also introduce the length of a
curve parametrized by a time scale parameter in ${\mathbb{R}}^{3}$ .

We study tubular surfaces in Euclidean 3-space satisfying some equations in terms of the Gaussian curvature, the mean curvature, the second Gaussian curvature, and the second mean curvature. This paper is a completion of Weingarten and linear Weingarten tubular surfaces in Euclidean 3-space.
1. Introduction
Let 𝑓 and 𝑔 be smooth functions on a sur...

In this paper, the Darboux rotation axis for a curve in Galilean and
Pseudo-Galilean spaces are decomposed into two simultaneous rotation. The axes of
these simultaneous rotations are joined by a simple mechanism. One of these axes is a
parallel of the principal normal of the curve, the direction of the other is the direction of the
Darboux vectors...

A special motion by the form Y = AX + C with one parameter has been given by [5] in Euclidean n space.
In this paper, we find a geometrical meaning for the determinant of the derivative matrices A*,A** and A*** according to Bishop frame in Minkowski 3space. Then we search, in this case, the geometry of the 1s t and 2 nd order acceleration pole poin...

We obtained an equation of the homothetic motion of any smooth semi-Euclidean submanifold M on its tangent plane at the contact points, along pole curves which are trajectories of instantaneous rotation centers at the contact points. Also, we gave some remarks for the homothetic motions that are both sliding and rolling at every moment. We establis...

In this study, we derive the equations of a motion model of two smooth homothetic along pole curves submanifolds M and N; the curves are trajectories of instantaneous rotation centers at the contact points of these submanifolds. We comment on the homothetic motions, which assume sliding and rolling.

In this study, we obtained an equation of homothetic motion of any smooth semi-Euclidean
submanifold M upon another N along common tangent plane at the contact points, along pole curves
which are trajectories of instantaneous rotation centers at the contact points and we gave some
remarks for the homothetic motions will be both sliding and rolling...

We define Bäcklund transformations of curves according to the Bishop frame which preserve the natural curvatures under certain assumptions in Euclidean 3-space.

## Questions

Question (1)

What is the contravariant derivative and what are the differences with covariant derivative?