Alo, JetaAkbıyık, Mücahit2026-01-312026-01-3120251367-0751https://doi.org/10.1093/jigpal/jzae039https://hdl.handle.net/20.500.12662/10513In 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.eninfo:eu-repo/semantics/closedAccess11R5214H5053A35Article10.1093/jigpal/jzae0392-s2.0-1050175591986Q233