In this paper, we obtain the necessary and sufficient conditions of a surface pencil pair
interpolating a Bertrand pair as common asymptotic curves in Euclidean 3-space E 3 …

A curve on a surface is a geodesic curve if its principal normal vector is anywhere aligned
with the surface normal. Using the Serret–Frenet frame, a timelike surface couple (TLSC) …

The main outcome of this work is the construction of a surface pencil with a similarity to
Bertrand curves in Euclidean 3-space E 3. Then, by exploiting the Serret–Frenet frame, we …

This paper is about deriving the necessary and sufficient conditions of a surface family pair
with a Bertrand pair as common geodesic curves in Galilean 3-space G 3. Thereafter, the …

In this paper, we derive the necessary and sufficient conditions of surface pencil pair
interpolating Bertrand pair as common asymptotic curves in Galilean space G3. Moreover …

In this paper, we define the necessary and sufficient conditions for a parametric surface on
which both the involute and evolute of any given curve lie to be geodesic, asymptotic and …

The main interest of this work is to construct surface family pair with the symmetry of Bertrand
pair in Euclidean 3-space $\mathbb {E}^{3} $. Then, by employing the Serret-Frenet frame …

A principal curve on a surface plays a paramount role in reasonable implementations. A
curve on a surface is a principal curve if its tangents are principal directions. Using the Serret …

The primary objective of this work is to discuss a surface family with the similarity of Bertrand
curves in 3D Galilean space. Subsequently, by applying the Serret–Frenet frame, we …

In this paper, we express surfaces parametrically through a given spacelike (timelike)
asymptotic curve using the Frenet frame of the curve in Minkowski 3-space. Necessary and …