The connection is a non-tensorial object that describes the covariant derivative in a non-Minkowski spacetime. The connection takes the antisymmetry of the commutator of covariant derivatives acting on any tensor, in the simplest case a vector. The commutator is antisymmetric, the connection is antisymmetric. There is no symmetric commutator so there is no symmetric connection. Paper 122 and the definitive proofs on the home page of this site have proven this in a way that any reader with mathematical training can understand. So this advance in scholarship has been accepted by the experienced and capable ECE readership. Wikipedia deliberately ignores the whole of this readership, and falsely asserts that the connection is symmetric. This symmetric connection is still referred to on Wikipedia as the Riemann, Christoffel or Levi-Civita connection. The use of such a connection led directly to complete disaster for twentieth century cosmology, which is based almost entirely on the incorrect Einstein field equation. In view of this, we have constructed on this site a plausible torsion based cosmology, which has been accepted by the ECE readership. So “authority in physics”, if such a thing ever exists, has been transferred away from the obsolete societies of physics, such as the Institute of Physics to the actual readership, the vast majority of scientists.

## Wikipedia Entries on the Connection of non-Minkowski Geometry

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