Some New Properties of Surfaces Generated by Null Cartan Curves

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International Electronic Journal of Geometry
Volume:15 Issue:1
Some New Properties of Surfaces Generated by Null Cartan Curves

Some New Properties of Surfaces Generated by Null Cartan Curves

Authors : Ayşe YAVUZ, Melek ERDOĞDU

Pages : 116-131

Doi:10.36890/iejg.963159

View : 40 | Download : 13

Publication Date : 2022-04-30

Article Type : Research Paper

Abstract :In this paper, some special types of surfaces with null Cartan base curve are investigated. The generating lines of the surfaces are chosen as a linear combination of Cartan frame fields with non-constant differentiable functions. Firstly, the surfaces whose generating lines have the same direction of Cartan frame fields B; N and T are examined respectively. As a special case, Gaussian and Mean curvatures of one parameter family of Bertrand curves of a given null Cartan curve and the singular points of this type of surface are stated. Furthermore, an example is also stated to explain the obtained results. Then, the surfaces with null Cartan base curve are investigated where generating lines lie on the planes spanned by insert ignore into journalissuearticles values(N, B);, insert ignore into journalissuearticles values(T,B); and insert ignore into journalissuearticles values(T, N); respectively. Finally, some differential geometric properties of these surface are given mainly in three different cases
Keywords : Cartan frame, Bertrand curve, null Cartan curve

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