In this study, we consider framed curves as regular or singular space curves with an adapted
frame in Euclidean 3-space. We define framed natural mates of a framed curve that are …

Associated with a Frenet curve α α in Euclidean 3-space E^ 3 E 3, there exists the notion of
natural mate β β of α α. In this article, we extend the natural mate β β to sequential natural …

The concept of the natural mate and the conjugate curves associated to a smooth curve in
Euclidian 3‐space were introduced initially by Dashmukh and others. In this paper, we give …

In this study, we introduce the natural mate and conjugate mate of a Frenet curve in a three
dimensional Lie group G with bi-invariant metric. Also, we give some relationships between …

In this work, we present a new Bishop frame for the conjugate curve of a curve in the 3-
dimensional Lie group G 3. With the help of this frame, we derive a parametric …

The main purpose in this study is to create the adjoint curve of a curve according to the
modified orthogonal frame created by torsion in Euclidean and Minkowski 3-space. Besides …

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 …

In this paper, we consider the Darboux frame of a curve α lying on an arbitrary regular
surface and we use its unit osculator Darboux vector D¯ o, unit rectifying Darboux vector D¯ …

In this study, we give a new curve pair that generalizes some of the famous pairs of curves
as Bertrand and constant torsion curves. This curve pair is defined with the help of a vector …

In this paper, we introduce new adjoint curves which are associated curves in Euclidean
space of three dimension. They are generated with the help of integral curves of special …