On constructing frames of a split octonionic curve with an associated spatial split octonionic curve

Abstract In this study, we first introduce the associated spatial split octonionic curve corresponding to a given split octonionic curve. Next, we construct a novel frame and derive its derivative formulas along a split octonionic curve using the G₂ -frame of the associated spatial split octonionic curve. This method is both time-efficient and computationally efficient. We also give the construction of the frame by using the Frenet–Serret frame of the associated curve. Furthermore, we provide MATLAB codes to compute the frame formulas of a split octonionic curve using the G₂ -frame of its associated spatial split octonionic curve. To demonstrate the practical application of our theoretical results, we present an example using symbolic computations performed in MATLAB.