Alo, JetaAkbiyik, Mucahit2025-03-092025-03-0920241367-07511368-9894https://doi.org/10.1093/jigpal/jzae039https://hdl.handle.net/20.500.12662/4678In this paper, we first define the vector product in Minkowski space $\mathbb{R}_{4}<^>{7}$ , which is identified with the space of spatial split-octonions. Next, we derive the $G_{2}-$ 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 $G_{2}-$ frame and Frenet-Serret frame. Furthermore, we present the Frenet-Serret frame with split octonions in $\mathbb{R}_{4}<^>{8}$ . Finally, we give illustrative examples with Matlab codes.eninfo:eu-repo/semantics/closedAccess53A3511R5214H50Article10.1093/jigpal/jzae039Q1WOS:001193084400001Q2