Best pair of two skew lines over the octonions
An octonion has a scalar part and a vector part. The pure octonions, i. e., all those with 0 as scalar part, can be isomorphically identified with \(\mathbb{R}^7\). Seven-dimensional space can then be endowed with a geometry, by defining points and lines in the usual manner, and defining line parallelism and orthogonality based on the dot and vector product of octonions. In this context, the authors determine the distance between two skew lines, i. e., the length of the shortest segment connecting them.
double vector cross product in \(\mathbb{R}^7\)
scientific article; zbMATH DE number 6484661