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 …

Page 1 International J.Math. Combin. Vol.1(2016), 1-7 N∗C∗− Smarandache Curve of
Bertrand Curves Pair According to Frenet Frame Süleyman Senyurt, Abdussamet Calıskan …

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 …

PROPERTIES OF INTEGRAL INVARIANTS OF THE INVOLUTE-EVOLUTE OFFSETS OF
RULED SURFACES Gülsüm Yeliz Sentürk1 §, Salim Yüce2 1, Page 1 International Journal …

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 …

In this study, we identify the instantaneous Pfaffi an vector of the closed motion defined
along the striction curve of the ruled surface φA which is a Mannheim offset of closed ruled …