Pontos helicoidais e vértices de Darboux de curvas no espaço euclidiano

Abstract

The main aim of this work is a study about twistings points and Darboux vertices of n-space curves. We define the concept of twisting of a n-space curve as flattening point of its tangent indicatrix and show that is equivalent to having higher order of contact with some generalized helix. In the three dimensional case we establish a relation between twisting points and Darboux vertices. We also obtain a version of the four vertex theorem for space closed curves involving such points.