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

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.