Ruled Surfaces Constructed by Planar Curves in Euclidean 3-Space with Density

Abstract

Öz: In the present study, firstly we recall the parametric expressions of planar curves with zero 𝜑�-curvaturein Euclidean 3-space with density 𝑒�𝑎�𝑥�1 and with the aid of the Frenet frame of these planar curves, weobtain the Smarandache curves of them. After that, we study on ruled surfaces which are constructed bythe curves with zero 𝜑�-curvature in Euclidean 3-space with density 𝑒�𝑎�𝑥�1 and their Smarandache curvesby giving the striction curves, distribution parameters, mean curvature and Gaussian curvature of theseruled surfaces. Also, we give some examples for these surfaces by plotting their graphs. We useMathematica when we are plotting the graphs of examples.