Ruled and Rotational Surfaces Generated by Non-Null Curves with Zero Weighted Curvature in $(mathbb{L}^{3},ax^{2}+by^{2})$

Authors : Mustafa ALTIN, Ahmet KAZAN, Hacı Bayram KARADAĞ

Pages : 11-29

Doi:10.36890/iejg.599817

View : 45 | Download : 8

Publication Date : 2020-10-15

Article Type : Research Paper

Abstract :In this study, firstly we give the weighted curvatures of non-null planar curves in Lorentz-Minkowski space with density e^insert ignore into journalissuearticles values(ax2+by2); and we obtain the planar curves whose weighted curvatures vanish in this space according to the cases of not all zero constants a and b. After giving the Frenet vectors of the non-null planar curves with zero weighted curvature in Lorentz-Minkowski space with density e^insert ignore into journalissuearticles values(ax2);, we create the Smarandache curves of them. With the aid of these curves and their Smarandache curves, we get the ruled surfaces whose base curves are non-null curves with vanishing weighted curvature and ruling curves are Smarandache curves of them. Followingly, we give some characterizations for these ruled surfaces by obtaining the mean and Gaussian curvatures, distribution parameters and striction curves of them. Also, rotational surfaces which are generated by non-null planar curves with zero weighted curvatures in Lorentz-Minkowski space E^3_1 with density e^insert ignore into journalissuearticles values(ax2+by2); are studied according to some cases of not all zero constants a and b. We draw the graphics of obtained surfaces.
Keywords : Weighted curvature, Lorentz Minkowski space, spacelike and timelike curves, ruled surface, rotational surface

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