In [14] Matsuda and Yorozu.explained that there is no special Bertrand curves in Eⁿ and they new kind of Bertrand curves called (1,3)-type Bertrand curves Euclidean space. In this paper , by using the similar methods given by Matsuda and Yorozu [14], we obtain that bitorsion of the quaternionic curve is not equal to zero in semi-Euclidean space E4^2. Obtain (N,B2) type quaternionic Bertrand cur...

This paper reports the study of properties of the curve pairs of the Bertrand types using our automated reasoning program based on Wu’s method of mechanical theorem proving for differential geometry. A complete list of results about Bertrand curves in metric and affine spaces is derived mechanically. The list includes most of the known results of various Bertrand curves. We also derive some new...

In the study of the fundamental theory and the characterizations of space curves, the related curves for which there exist corresponding relations between the curves are very interesting and important problems. The most fascinating examples of such curve are associated curves, the curves for which at the corresponding points of them one of the Frenet vectors of a curve coincides with the one of...

We investigated differential geometries of Bertrand curves and Mannheim in a three-dimensional sphere. clarify the conditions for regular spherical to become curves. Then, we concentrate on singular As curves, considered framed define give

In this paper, we investigate the surfaces generated by binormal motion of Bertrand curves, which is called Razzaboni surface, in Minkowski 3-space. We discussed the geometric properties of these surfaces in M according to the character of Bertrand geodesics. Then, we define the Razzaboni transformation for a given Razzaboni surface. In other words, we prove that there exists a dual of Razzabon...

In this paper, the curvature and torsion of Smarandache curves obtained by vectors Bertrand partner curve are calculated. These values expressed depending upon curve. Besides, we illustrate example with our main results.