Serret-Frenet formulas for octonionic curves

Abstract

In this paper, we dene spatial octonionic curves (SOC) in R7 and octonionic curves (OC) in R8 by using octonions. Firstly, we determine Serret-Frenet equations, and curvatures of the SROC in R7. Then, Serret-Frenet equations for the OC in R8 are calculated with the help of Serret-Frenet equations of SOC in R7.

Keywords

• Serret-Frenet formulas
• spatial octonionic curve
• octonionic curve
• curvature
• torsion