Special Space Curves Characterized by $\det(α^{(3)}, α^{(4)}, α^{(5)}) = 0$

  • S. Saracoglu
  • Y. Yayli Ankara Univ., Turkey


By using the facts that the condition$\det(α^{(1)}, α^{(2)}, α^{(3)}) = 0$ characterizes a plane curve and the condition $\det(α^{(2)}, α^{(3)}, α^{(4)}) = 0$ characterizes a curve of constant slope, we present special space curves characterized by the condition $\det(α^{(3)}, α^{(4)}, α^{(5)}) = 0$, in different approaches. It is shown that the space curve is Salkowski if and only if $\det(α^{(3)}, α^{(4)}, α^{(5)}) = 0$. The approach used in our investigation can be useful in understanding the role of the curves characterized by $\det(α^{(3)}, α^{(4)}, α^{(5)}) = 0$ in differential geometry.
How to Cite
Saracoglu, S., and Y. Yayli. “Special Space Curves Characterized by $\det(α^{(3)}, α^{(4)}, α^{(5)}) = 0$”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 4, Apr. 2014, pp. 571-6, http://umj.imath.kiev.ua/index.php/umj/article/view/2160.
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