Framed Curves and Their Applications Based on a New Differential Equation

Authors : Bahar DOĞAN YAZICI, Sıddıka ÖZKALDI KARAKUŞ, Murat TOSUN

Pages : 47-56

Doi:10.36890/iejg.875477

View : 9 | Download : 5

Publication Date : 2022-04-30

Article Type : Research Paper

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 $p,q\neq 0$ framed curvatures in Euclidean space. Next, we give the relationships between this differential equation and some special curves. Moreover we intoduce a new equation of framed helices with the help of this differential equation. Moreover, these are support by some examples and figures.
Keywords : framed curves, framed spherical curves, framed helices, framed rectifying curves, singular points