On split-octonionic curves

In this paper, we first define the vector product in Minkowski space R<inf>4</inf>7, which is identified with the space of spatial split-octonions. Next, we derive the G<inf>2</inf>- 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 G<inf>2</inf>- frame and Frenet–Serret frame. Furthermore, we present the Frenet–Serret frame with split octonions in R<inf>4</inf>8. Finally, we give illustrative examples with Matlab codes. © The Author(s) 2024. Published by Oxford University Press. All rights reserved.