This is a coordinate independent, generally covariant geometry equivalent to Riemann geometry but with well known advantages (S. P. Carroll, “Spacetime and Geometry: an Introduction to General Relativity” (Addison Wesley, New York, 2004, and free downloadable notes), chapter 3. Professor Carroll taught it at Harvard, UCSB and Chicago. Riemann geometry reduces to Minkowski geometry for a particular metric, and Minkowski geometry reduces to Euclidean 3-D geometry in the non-relativistic limit. So any talk of Cartan geometry being “incorrect” is absurd, because it would mean that the other geometries mentioned here are “incorrect”. ECE is based directly on the textbook by Carroll, chapter three. Any talk of ECE’s geometry being “incorrect ” may be dismissed entirely as unreliable. Paper 137 for example is a precise, self checking proof of the correctness of Cartan’s geometry in the form of the Cartan Evans identity.

## Standard Cartan Geometry

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