Rotational Surfaces Generated by Planar Curves in E3 with Density

Abstract

In this paper, we obtain the parametric expressions of curves which have zero weighted curvature in a plane with density $e^{ax+by}$ and create the Smarandache curves of the obtaining curves. Also, we construct the rotational surfaces which are generated by planar curves with vanishing weighted curvature and give some characterizations for them.