Bertrand Curves of AW( k

We consider curves of AW(k)-type (1≤k≤3) in the equiform geometry of the Galilean space G3. We give curvature conditions of curves of AW(k)-type. Furthermore, we investigate Bertrand curves in the equiform geometry of G3. We have shown that Bertrand curve in the equiform geometry of G3 is a circular helix. Besides, considering AW(k)-type curves, we show that there are Bertrand curves of weak AW(2)-type and AW(3)-type. But, there are no such Bertrand curves of weak AW(3)-type and AW(2)-type

TUBULAR SURFACES WITH DARBOUX FRAME IN GALILEAN 3-SPACE

In this paper, we define tubular surface by using a Darboux frame instead of a Frenet frame. Subsequently, we compute the Gaussian curvature and the mean curvature of the tubular surface with a Darboux frame. Moreover, we obtain some characterizations for special curves on this tubular surface in a Galilean 3-space

Bertrand and Mannheim Partner -curves on Parallel Surfaces

In this paper we study Bertrand and Mannheim partner -curves on parallel surface. Using the definition of parallel surfaces, first we find images of two curves lying on two different surfaces and satisfying the conditions to be Bertrand partner -curve or Mannheim partner -curve. Then we obtain relationships between Bertrand and Mannheim partner -curves and their image curves

On Characterization of Inextensible Flows of Curves According to Type-2 Bishop Frame E3

In this paper, we study inextensible flows of curves according to type-2 Bishop frame in Euclidean 3-space. Necessary and sufficient conditions for an inextensible curve flow are expressed as a partial differential equation involving the curvature