Differential Equations for a Space Curve According to the Unit Darboux Vector

Abstract

In this work, the differential equation of a differentiable curve is expressed, by making use of Laplace and normal Laplace operators, as a linear combination of the unit Darboux vector defined as C = sinφT + cosφB of that curve. Later, the necessary and sufficient conditions are given for the space curves to be a 1-type Darboux vector.