| Summary: | This study investigates curves in a 7-dimensional space, represented by spatial generalized octonion-valued functions of a single variable, where the general octonions include real, split, semi, split semi, quasi, split quasi, and para octonions. We begin by constructing a new frame, referred to as the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>2</mn></msub></semantics></math></inline-formula>-frame, for spatial generalized octonionic curves, and subsequently derive the corresponding derivative formulas. We also present the connection between the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>2</mn></msub></semantics></math></inline-formula>-frame and the standard orthonormal basis of spatial generalized octonions. Moreover, we verify that Frenet–Serret formulas hold for spatial generalized octonionic curves. We establish the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>2</mn></msub></semantics></math></inline-formula>-congruence of two spatial generalized octonionic curves and present the correspondence between the Frenet–Serret frame and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>2</mn></msub></semantics></math></inline-formula>-frame. A key advantage of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>2</mn></msub></semantics></math></inline-formula>-frame is that the associated frame equations involve lower-order derivatives. This method is both time-efficient and computationally efficient. To demonstrate the theory, we present an example of a unit-speed spatial generalized octonionic curve and compute its <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>G</mi><mn>2</mn></msub></semantics></math></inline-formula>-frame and invariants using MATLAB.
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