In this paper, we study biharmonic constant Π₁- slope curves according to type-2 Bishop frame in the SOL³. We characterize the biharmonic constant Π₁- slope curves in terms of their Bishop curvatures. Finally, we find out their explicit parametric integral equations in the SOL³.
In this work, we investigate relationships between Darboux and type-2 Bishop frames in Euclidean space. Then, we obtain the geodesic curvature of the spherical image curve of the Darboux vector of the type-2 Bishop frame. Also, we give transition matrix between the Darboux and type-2 Bishop frames of the type-2 Bishop frames of the spherical images of the edges [Formula: see text] and [Formula: see text]. Finally, we express some interesting relations and illustrate of the examples by the aid Maple programe.
In this paper, we obtain the Fermi-Walker derivatives of , , magnetic curves according to the type-2 Bishop frame in the space. Moreover, we obtain the energy of the Fermi-Walker derivative of magnetic curves according to the type-2 Bishop frame in space. Finally, we have energy relations of some vector fields associated with type-2 Bishop frame in the space.
In this paper, we define and investigate a special kind of ruled surfaces called type-2 Smarandache ruled surfaces related to the type-2 Bishop frame in
E
3
. From this point and depending on the type-2 Bishop curvature, we provide the necessary and sufficient conditions that allow these surfaces to be developable in a minimal amount of time. Furthermore, an example is given to clear the results.