Ruled surfaces in $E^{3}$ with density

In the present paper, we study curves in $\mathbb{E}^{3}$ with density $e^{ax^{2}+by^{2}},$ where $a,b\in \mathbb{R}$ not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanish...

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Veröffentlicht in:Honam mathematical journal 2019, 41(4), , pp.683-695
Hauptverfasser: Mustafa Altin, Ahmet Kazan, H.Bayram Karadag
Format: Artikel
Sprache:eng
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Zusammenfassung:In the present paper, we study curves in $\mathbb{E}^{3}$ with density $e^{ax^{2}+by^{2}},$ where $a,b\in \mathbb{R}$ not all zero constants and give the parametric expressions of the curves with vanishing weighted curvature. Also, we create ruled surfaces whose base curves are the curve with vanishing weighted curvature and the ruling curves are Smarandache curves of this curve. Then, we give some characterizations about these ruled surfaces by obtaining the mean curvatures, Gaussian curvatures, distribution parameters and striction curves of them. KCI Citation Count: 0
ISSN:1225-293X
2288-6176