ON HYBRID CURVES

Abstract

In this paper, we first define the vector product in a special analog Minkowski Geometry $(\mathbb{R}^3,\langle,\rangle) $ which is identified with the space of spatial hybrids. Next, we derive the Frenet-Serret frame formulae for a three dimensional non-parabolic curve by using the spatial hybrids and the vector product. However, we present the Frenet-Serret Frame formulae of a non-lightlike hybrid curve in $\mathbb{R}^4$ and an illustrative example for all theorems of the paper with Matlab codes.