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

Avi Rabinowitz

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arXiv · 1902.01696

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

Avi Rabinowitz

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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.

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BibTeX RIS

Avi Rabinowitz. 2019-01-20. Intriguing & intuitive relation of diagonal Riemann tensor components to the corresponding 2-d Gaussian curvature for diagonal metrics of any dimensionality. https://arxiv.org/abs/1902.01696

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