For each Frenet curve $\alpha $ in the Euclidean 3-space $\mathbb {E}^{3} $, there exists a
unique unit speed curve $\beta $ tangent to the principal normal vector field of $\alpha $. We …

arxiv:1905.04540v1 [math.DG] 11 May 2019 Page 1 RECTIFYING-TYPE CURVES AND
ROTATION MINIMIZING FRAME Rn ÖZGÜR KESKIN* AND YUSUF YAYLI Abstract. In this …

The aim of this paper is to prove that the distance function of every Frenet curve in G 3
satisfies a 4-th order differential equation. Also, we show that if α is a unit speed Frenet curve …

In this paper, we define some new vector fields along a space curve with nonvanishing
curvatures in Euclidean 4-space. By using these vector fields we determine some new …

In this paper, we develop a method to obtain the lines of curvature on parametric
hypersurfaces in Euclidean 4-space. We show that such lines are the solutions to systems of …

We derive a general differential equation satisfed by the distance function for quaternionic
curves in Euclidean 4-space. By using this differential equation, we express …

In this paper, we give the definition of the natural mate of a non-null Frenet curve in
Minkowski 3-spaces. The main purpose of this paper is to prove some relationships between …

For each non-null Frenet curve\gamma in Minkowski 3-space, there exists a unique unit
speed non-null curve tangent to the principal binormal vector field of\gamma. We briefly call …