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

#### Mustafa ALTIN [1] , Ahmet KAZAN [2] , H.bayram KARADAĞ [3]

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.

Ruled surfaces, Smarandache curves, Weighted curvature
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Birincil Dil en Makaleler Orcid: 0000-0001-5544-5910Yazar: Mustafa ALTIN (Sorumlu Yazar)Kurum: BİNGÖL ÜNİVERSİTESİ, BİNGÖL TEKNİK BİLİMLER MESLEK YÜKSEKOKULUÜlke: Turkey Orcid: 0000-0002-1959-6102Yazar: Ahmet KAZAN Kurum: MALATYA TURGUT ÖZAL ÜNİVERSİTESİÜlke: Turkey Orcid: 0000-0001-6474-877XYazar: H.bayram KARADAĞ Kurum: İNÖNÜ ÜNİVERSİTESİÜlke: Turkey Inonu University FDK-2018-1349 We're very much thankful to Inonu University BAP (Scientific Research Projects) unit for their support to our this study. Yayımlanma Tarihi : 27 Mart 2020
 Bibtex @araştırma makalesi { cbayarfbe632176, journal = {Celal Bayar University Journal of Science}, issn = {1305-130X}, eissn = {1305-1385}, address = {}, publisher = {Celal Bayar Üniversitesi}, year = {2020}, volume = {16}, pages = {81 - 88}, doi = {}, title = {Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density}, key = {cite}, author = {ALTIN, Mustafa and KAZAN, Ahmet and KARADAĞ, H.bayram} } APA ALTIN, M , KAZAN, A , KARADAĞ, H . (2020). Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density. Celal Bayar University Journal of Science , 16 (1) , 81-88 . Retrieved from https://dergipark.org.tr/tr/pub/cbayarfbe/issue/53288/632176 MLA ALTIN, M , KAZAN, A , KARADAĞ, H . "Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density". Celal Bayar University Journal of Science 16 (2020 ): 81-88 Chicago ALTIN, M , KAZAN, A , KARADAĞ, H . "Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density". Celal Bayar University Journal of Science 16 (2020 ): 81-88 RIS TY - JOUR T1 - Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density AU - Mustafa ALTIN , Ahmet KAZAN , H.bayram KARADAĞ Y1 - 2020 PY - 2020 N1 - DO - T2 - Celal Bayar University Journal of Science JF - Journal JO - JOR SP - 81 EP - 88 VL - 16 IS - 1 SN - 1305-130X-1305-1385 M3 - UR - Y2 - 2020 ER - EndNote %0 Celal Bayar Üniversitesi Fen Bilimleri Dergisi Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density %A Mustafa ALTIN , Ahmet KAZAN , H.bayram KARADAĞ %T Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density %D 2020 %J Celal Bayar University Journal of Science %P 1305-130X-1305-1385 %V 16 %N 1 %R %U ISNAD ALTIN, Mustafa , KAZAN, Ahmet , KARADAĞ, H.bayram . "Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density". Celal Bayar University Journal of Science 16 / 1 (Mart 2020): 81-88 . AMA ALTIN M , KAZAN A , KARADAĞ H . Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density. Celal Bayar Univ J Sci. 2020; 16(1): 81-88. Vancouver ALTIN M , KAZAN A , KARADAĞ H . Ruled Surfaces Constructed by Planar Curves In Euclidean 3-Space With Density. Celal Bayar University Journal of Science. 2020; 16(1): 88-81.

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