I can see why we want a connection on a Riemannian manifold to be compatible with the metric. But why do we want our connections to be torsion-free? Why do we even care about torsion? Is it just to get uniqueness of the Riemannian connection?
2026-04-08 19:41:52.1775677312
Why do we want connections on (Riemannian) manifolds to be torsion-free?
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