In this article, we look at a surface associated with real‐valued functions. The surface is
known as a harmonic surface, and its unit normal vector and mean curvature have been …

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, we have investigated Hasimoto surfaces with a pointwise 1-type Gauss map,
which will be useful in classifying surfaces. Firstly, we have reminded the basic concepts …

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, we investigate Hasimoto surfaces considering the modified orthogonal frame.
Firstly, we recall the relations between the Frenet frame and the modified orthogonal frame …

In this paper, we present the evolutions of the ruled surfaces constructed by the tangent,
normal-like, and binormal-like vector fields of a polynomial space curve. These evolutions of …

In the present study, we work on the Hasimoto surfaces in three-dimensional Euclidean
space by using q-frame. Calculating the coefficients of fundamental forms, we present …