In this paper, we analyzed surfaces family possessing a Mannheim partner curve of a given
curve as a geodesic. Using the Frenet frame of the curve in Euclidean 3-space, we express …

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 …

In this paper, we construct a surface family possessing a Mannheim B-pair of a given curve
as an asymptotic curve. Using the Bishop frame of the given Mannheim B curves, we present …

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 …

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 …

Developable surface is widely used in the design and machining of industrial products. In
this paper, developable surface pencil pairs with Natural pair and Conjugate pair …