Natural Intrinsic Geometrical Symmetries

TL;DR

This paper proposes a new class of homogeneous but non-isotropic Riemannian spaces, expanding the understanding of natural symmetrical geometries beyond constant curvature spaces.

Contribution

It introduces a novel class of homogeneous, non-isotropic Riemannian spaces that are considered the most natural symmetrical spaces beyond constant curvature models.

Findings

Defines the class of natural intrinsic geometrical symmetries

Characterizes spaces that are homogeneous but not isotropic

Extends the concept of symmetry beyond classical constant curvature spaces

Abstract

A proposal is made for what could well be the most natural symmetrical Riemannian spaces which are homogeneous but not isotropic, i.e. of what could well be the most natural class of symmetrical spaces beyond the spaces of constant Riemannian curvature, that is, beyond the spaces which are homogeneous and isotropic, or, still, the spaces which satisfy the axiom of free mobility.