Murat Bekar

N-Legendre and N-slant curves in the unit tangent bundle of Minkowski surfaces

Let

Semi-Euclidean quasi-elliptic planar motion

(\mathbb{M}_{1}^{2},g)

Ruled Surfaces and Tangent Bundle of Unit 2-Sphere

be a Minkowski surface and

Involutions in Semi-Quaternions

(T_1\mathbb{M}_1^2, g_1)

Involutions of Complexified Quaternions and Split Quaternions

its unit tangent bundle endowed with the pseudo-Riemannian induced Sasaki metric. We extend in this paper the study of the N-Legendre and N-slant curves which the inner product of normal vector and Reeb vector is zero and nonzero constant respectively in

Dual Quaternion Involutions and Anti-Involutions

\left( T_1 \mathbb{M}_1^2, g_1 \right)

Slant Helix Curves and Acceleration Centers in Minkowski 3-Space Ε 3 1

, given in \cite{hmy}, to the Minkowski context and several important characterizations of these curves are given.\newline

Involutions in Dual Split-Quaternions

The aim of this paper is to study the algebra of split semi-quaternions with their basic properties. Also, the results of the Euclidean planar motion given by Blaschke and Grunwald is generalized to semi-Euclidean planar motion by using the algebra of split semi-quaternions.

Involutions in split semi-quaternions

In this paper, a one-to-one correspondence is given between the tangent bundle of unit 2-sphere, T𝕊2, and the unit dual sphere, 𝕊𝔻2. According to Study’s map, to each curve on 𝕊𝔻2 corresponds a rul...

N-Legendre and N-slant curves in the unit tangent bundle of surfaces

Communicated by Abraham Ungar Abstract. Involutions are self-inverse and homomorphic linear mappings. Rotations, reflections and rigid-body (screw) motions in three-dimensional Euclidean space R can be represented by involution mappings obtained by quaternions. For example, a reflection of a vector in a plane can be represented by an involution mapping obtained by real-quaternions, while a reflection of a line about a line can be represented by an involution mapping obtained by dual-quaternions. In this paper, we will consider two involution mappings obtained by semi-quternions, and a geometric interpretation of each as a planar-motion in R.