Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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RULED SURFACES IN E3 WITH DENSITY

  • Altin, Mustafa (Technical Sciences Vocational School, Bingol University) ;
  • Kazan, Ahmet (Department of Computer Technologies, Dogansehir Vahap Kucuk Vocational School of Higher Education, Malatya Turgut Ozal University) ;
  • Karadag, H.Bayram (Department of Mathematics, Faculty of Arts and Sciences, Inonu University)
  • Received : 2019.01.12
  • Accepted : 2019.03.06
  • Published : 2019.12.25
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Abstract

In the present paper, we study curves in 𝔼3 with density $e^{ax^2+by^2}$, where a, b ∈ 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.

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Acknowledgement

Supported by : Inonu University

This study has been supported by BAP (Scientific Research Projects) unit under the Project number FDK-2018-1349 at Inonu University, Malatya, TURKEY.

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