Geometry of n-dimensional Euclidean space Gaussian enfoldments

摘要

In this study the geometric features and relationships of the points contained into a Gaussian enfoldment of n-dimensional Euclidean space are analyzed. Euclidean distances and angles are described by means of a simple formulation, which demonstrates the topological change underwent by n-dimensional Euclidean spaces upon Gaussian enfoldment, transforming the Euclidean points into enfoldment points lying in a closed sphere of unit radius. This property relates Gaussian enfoldments with the holographic electronic density theorem.