Framed Curves and Their Applications Eased on a New Differential Equation

Abstract

Characterization is very important for non-regular curves in differential geometry. Recently, the concept of framed curve has been proposed to examine a non-regular curve. Framed curves are defined as smooth curves with a moving frame that can have singular points. In this paper, the differential equation is obtained by using distance squared functions for framed curves with for each p, q not equal 0 framed curvatures in Euclidean space. Next, we give the relationships between the differential equation and some special curves. Moreover we introduce a new equation of framed helices with the help of the differential equation. Moreover, these are supported by some examples and figures.