Treffer: On split-octonionic curves.

In 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. [ABSTRACT FROM AUTHOR]

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