The Alpha Group Tensorial Metric

Abstract: The Alpha Group is an abstract geometry group in $\mathbb{R}^4$. The way it was conceived allows a new interpretation of the structure of hypercomplex space, with a new geometry and spatial topology, and a meaning for the geometric representation of $\mathbb{R}^4$ space to infinity. Therefore, it has been described as the tensorial metric formula in the Alpha Group. It will be shown that the Riemannian and Euclidean distance metrics between infinitesimal surfaces are represented as special cases of the metric of the Alpha Group.