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

Abstract

In this study, by using the facts that det(α^{(1)}, α^{(2)}, α^{(3)}) = 0 characterizes plane curve, and det(α^{(2)}, α^{(3)}, α^{(4)}) = 0 does a curve of constant slope, we give the special space curves that are characterized by det(α^{(3)}, α^{(4)}, α^{(5)}) = 0, in different approaches. We find that the space curve is Salkowski if and only if det(α^{(3)}, α^{(4)}, α^{(5)}) = 0. The approach we used in this paper is useful in understanding the role of the curves that are characterized by det(α^{(3)}, α^{(4)}, α^{(5)})=0 in differential geometry.

7 pages, 1 figure