In this article, we examine the relationship between Darboux frames along parameter curves
and the Darboux frame of the base curve of the ruled surface. We derive the equations of the …

Bertrand curves are a pair of curves that have a common principal normal vector at any point
and are related to symmetry properties. In the present paper, we define the notion of 1, 3-V …

This work examines some classical results of Bertrand curves for timelike ruled and
developable surfaces using the E. Study map. This provides the ability to define two timelike …

In this paper, we investigate and specify the Bertrand offsets of slant ruled and developable
surfaces in Euclidean 3-space E 3. This is accomplished by utilizing the symmetry of slant …

In this paper, the vectorial moments of the alternative vectors are expressed in terms of
alternative frame. According to the new versions of these vectorial moments, the parametric …

In this study, using Darboux frame {T, g, n} of ruled surface ϕ (s, v), the evolute offsets
ϕ^{∗}(s, v) with Darboux frame {T^{∗}, g^{∗}, n^{∗}} of ϕ (s, v) are defined. Characteristic …

Dual representations of the Bertrand offset-surfaces are specified and several new results
are gained in terms of their integral invariants. A new description of Bertrand offsets of …

On the evolute offsets of ruled surfaces in Minkowski 3-space Page 1 Turkish Journal of
Mathematics Volume 40 Number 3 Article 9 1-1-2016 On the evolute offsets of ruled …

This work extends some classical results of Bertrand curves to timelike ruled and
developable surfaces using the E. Study map. This provides support to define two timelike …

In this paper using the Blaschke approach we generalized the Bertrand curves to spacelike
ruled and developable surfaces. It is proved that, every spacelike ruled surface have a …