Intriguing & intuitive relation of diagonal Riemann tensor components to the corresponding 2-d Gaussian curvature for diagonal metrics of any dimensionality

Abstract

Using Gauss's square-roots of the metric components, the diagonal Riemann tensor components for diagonal metrics are calculated. The result is a form which makes their source in the metric directly intuitive and displays an intriguing relation to Gaussian curvature. Several examples of calculation utilizing this formula are presented, and a speculative quesiton is raised about the possibility of an invariant characteristic to spaces amenable to orthogonal coordinates/diagonal metrics.