Dual Smarandache curves and ruled surfaces obtained from the alternative frame

Year 2022, Volume: 12 Issue: 2, 512 - 526, 15.04.2022

Hatice Kusak Samancı , Veysi Cengiz

https://doi.org/10.17714/gumusfenbil.1004096

Abstract

According to the E-Study theorem, the dual Smarandache curve chosen on the dual unit sphere in dual space corresponds to the ruled surface formed by the directional lines in the Euclidean 3-space. In this study, some characterizations of ruled surfaces corresponding to dual Smarandache curves constructed with the help of dual components of the alternative frame are investigated.

Keywords

Alternative frame, Dual curve, Dual Smarandache curve, Dual space, E-Study teorem, Smarandache curve

Alternatif çatıdan elde edilen dual Smarandache eğrileri ve regle yüzeyleri

Abstract

E-Study teoremi gereği dual uzayda dual birim küre üzerinde seçilen dual Smarandache eğrisi Öklid-3 uzayındaki yönlü doğruların oluşturmuş olduğu regle yüzeye karşılık gelir. Bu çalışmada alternatif çatının dual bileşenlerinin yardımıyla oluşturulan dual Smarandache eğrilerine karşılık gelen regle yüzeylerine ait bazı karakterizasyonlar incelenmiştir.

Keywords

Alternatif çatı, Dual eğri, Dual Smarandache eğrisi, Dual uzay, E-Study teoremi, Smarandache eğrisi

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