Special space curves characterized by det(α⁽³⁾,α⁽⁴⁾,α⁽⁵⁾)=0 - Saracoglu, S.; Yayli, Y. (Український математичний журнал, 2014)
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.