On split-octonionic curves

Abstract In this paper, we first define the vector product in Minkowski space R₄^7, which is identified with the space of spatial split-octonions. Next, we derive the G₂- frame formulae for a seven dimensional Minkowski curve by using the spatial split-octonions and the vector product. We show that Frenet–Serret formulas are satisfied for a spatial split octonionic curve. We obtain the congruence of two spatial split octonionic curves and give relationship between the G₂- frame and Frenet–Serret frame. Furthermore, we present the Frenet–Serret frame with split octonions in R₄^8. Finally, we give illustrative examples with Matlab codes.