Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density

Abstract

In the present study, firstly we recall the parametric expressions of planar curves with zero phi-curvature in Euclidean 3-space with density e^ax_1 and with the aid of the Frenet frame of these planar curves, we obtain the Smarandache curves of them. After that, we study on ruled surfaces which is constructed by curves with zero -curvature in Euclidean 3-space with density e^ax_1 and their Smarandache curves by giving the striction curves, distribution parameters, mean curvature and Gaussian curvature of these ruled surfaces. Also, we give some examples for these surfaces by plotting their graphs. We use Mathematica when we are plotting the graphs of examples.

Keywords

• Ruled surfaces,Smarandache curves,Weighted curvature

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