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 …

There are many studies on regular rectifying curves in classical differential geometry, and
important results have been obtained. However, these studies are limited for a smooth curve …

The position vector field is the most elementary and natural geometric object on a Euclidean
submanifold. The position vector field plays important roles in physics, in particular in …

This paper gives new characteristic properties of non-null spherical and rectifying curves in
Minkowski 3-space E 1 3. In the light of the causal characteristics, we give some …

Some characterizations of non-null rectifying curves in dual Lorentzian 3-space D3 Page 1
http://www.aimspress.com/journal/Math AIMS Mathematics, 6(3): 2114–2131. DOI: 10.3934/math.2021129 …

This paper gives new characteristic properties of non-null spherical and rectifying curves in
Minkowski 3-space E 1 3. In the light of the causal characteristics, we give some …

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 study, we developed a mathematical framework for studying spherical and null curves
in dual Lorentzian 3‐space D 1 3. Considering the causal character of the dual curve …

In Euclidean 3-space, a family of curves, the co-successor, is motivated and then introduced
in relation to the natural mate. A complete characterization of co-successors is proved …

In this work, we prove that the ratio of torsion and curvature of any dual rectifying curve is a
non-constant linear function of its dual arc length parameter. Thereafter, a dual differential …