Mathematics – Differential Geometry
Scientific paper
2012-01-30
Mathematics
Differential Geometry
7 pages, 1 figure
Scientific paper
In this study, by using the facts that det({\alpha}^{(1)}, {\alpha}^{(2)}, {\alpha}^{(3)}) = 0 characterizes plane curve, and det({\alpha}^{(2)}, {\alpha}^{(3)}, {\alpha}^{(4)}) = 0 does a curve of constant slope, we give the special space curves that are characterized by det({\alpha}^{(3)}, {\alpha}^{(4)}, {\alpha}^{(5)}) = 0, in different approaches. We find that the space curve is Salkowski if and only if det({\alpha}^{(3)}, {\alpha}^{(4)}, {\alpha}^{(5)}) = 0. The approach we used in this paper is useful in understanding the role of the curves that are characterized by det({\alpha}^{(3)}, {\alpha}^{(4)}, {\alpha}^{(5)})=0 in differential geometry.
Saracoglu Semra
Yayli Yusuf
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