Euclidean, Pseudo-Euclidean, Conformal and Pseudoconformal Geometries

Abstract

In 0.5.3 we have defined the real Euclidean space R ⁿ as the affine space E ⁿ whose vectors satisfy axioms E.1° – 5°. Since the inner product x ² of a vector x = x ² e _i of this space by itself is a positive definite quadratic form x ² = e _ij x ⁱ x ^j , this space is also called a quadratic Euclidean space. In 0.5.3 we have seen that the space R ⁿ also satisfies the axioms M.1° – 3° of a metric space.