This work aims at investigating the geometry of surfaces corresponding to the geometry of
solutions of the vortex filament equation in Euclidean 3-space E 3 using the quasi-frame. In …

The main scope of this paper is to examine the smoke ring (or vortex filament) equation
which can be viewed as a dynamical system on the space curve in E³. The differential …

A surface M2 with position vector r= r (s, t) is called a Hasimoto surface if the relation rt= rs∧
rss holds. In this paper, we first define the Beltrami-Laplace operator according to the three …

The position vector of the surface r= r (s, t) is called Hasimoto surface if the relation rt= rs∧
rss hold. In this paper Hasimoto surfaces in Euclidean space E3 will be introduced …

In this study, firstly by considering the evolution of a moving space curve, we give some
related definitions and some new results about Hasimoto surfaces in Euclidean 3-spaces …

In this study, we examine some properties of Salkowski curves in E^3. We then make sense
of the angle (nt) in the parametric equation of the Salkowski curves. We provide the …

In this paper, the key issue we address here is the Hasimoto transformation in three-
dimensional Euclidean space, which allows us to specify the magnetic trajectory for the …

The non-linear Schr\"{o}dinger equation associated with the soliton surfaces in Minkowski 3-space
Page 1 http://www.aimspress.com/journal/Math AIMS Mathematics, 7(10): 17879–17893. DOI …

The movement of a thin vortex in a thin viscous fluid by the motion of a curve propagating in
Lorentz–Minkowski space E 1 3 is described by the vortex filament or smoke ring equation …

In this study, alternative, type-1 Bishop, type-2 Bishop and N-Bishop frames of Salkowski
curves in E3 are calculated. Moreover, curvatures, Darboux and pol vectors of these frames …