Generalized Similar Frenet Curves

Abstract

The paper is devoted to differential geometric invariants determining a Frenet curve in En up to a direct similarity. These invariants can be presented by the Euclidean curvatures in terms of an arc lengths of the spherical indicatrices. Then, they expressed by focal curvatures of the curve. And then, we give the relationship between curvatures of evolute curve and shape curvatures. Morever, the geometric interpretations of these invariants are given.