نوع مقاله : مقاله پژوهشی
عنوان مقاله English
نویسندگان English
In this paper, we present a generalization of the evolute of a curve in the plane and study its geometry. Consider a curve in the plane, denoted by $\gamma$, with curvature $\kappa$. If f is a smooth real-valued function, we define the spatial curve $\gamma_{f}$ in such a way that it is the generalization of the evolute of $\gamma$. The process of obtaining this curve is through the introduction of an angular surface. Theorem 2 shows that the singular points of $\gamma_{f}$ correspond to the vertices of $\gamma$ and are independent of the choice of the function $f$. In such points, the generalized evolute has a cusp singularity if and only if the curve $\gamma$ has a regular vertex at $s=s_0$. Furthermore, we investigate the contact of the generalized evolute $\gamma_f$ with a sphere and a plane. Additionally, by introducing a certain type of parallel curve, we study its geometric properties.
کلیدواژهها English
