In this article, we examine the relationship between Darboux frames along parameter curves
and the Darboux frame of the base curve of the ruled surface. We derive the equations of the …

In the present paper, we investigate the geometric properties of the linearly polarized light
wave (LPLW) and the homothetic motion of the polarization plane traveling in optical fiber in …

In this paper, we define a quaternionic operator whose scalar part is a real parameter and
vector part is a curve in three dimensional real vector space R 3. We prove that quaternion …

In this paper, we introduce a new vector space, the three-dimensional geometric real vector
space ℝ 3 (G), and a new number system, multiplicative quaternions ℍ (G). We give some …

Circular surfaces are smooth one-parameter families of circles. This paper includes three
main purposes about circular surfaces and roller coaster surfaces defined as circular …

In the present paper, we give a generalization for the magnetic flux tubes. Firstly, we define
the flux tube via quaternions. We obtain the magnetic flux canal surfaces and flux tubes by …

In this paper, we aim a kinematic method to investigate the behavior of polarized light in an
optical fiber. Geometric phase equations are obtained using elliptic quaternions. The …

In this paper, we introduce canal surfaces determined by spherical indicatrices of any spatial
curve in Minkowski 3-space by means of timelike split quaternions. Moreover, using …

In this paper, we analyze the homothetic motion of the polarization plane traveling along the
linearly polarized light wave ((LPL)-wave) in the optical fiber on the condition that the angle …

The aim of the paper is to present a new geometric viewpoint for magnetic flux tubes (MFTs)
in the three-dimensional Lorentzian space through split quaternion algebra. For this, we …