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

Abstract

By using the facts that the condition det(alpha((1)) , alpha((2)) , alpha((3))) =0 characterizes a plane curve and the condition det(alpha((2)) , alpha((3)) , alpha((4))) =0 characterizes a curve of constant slope, we present special space curves characterized by the condition det(alpha((3)) , alpha((4)) , alpha((5))) =0, in different approaches. It is shown that the space curve is Salkowski if and only if det(alpha((3)) , alpha((4)) , alpha((5))) =0. The approach used in our investigation can be useful in understanding the role of the curves characterized by det(alpha((3)) , alpha((4)) , alpha((5))) =0 in differential geometry.