The *fundamental theorem of Riemannian geometry* is the theorem which states that on a pseudo-Riemannian manifold there is a unique metric-compatible affine connection with vanishing torsion – the *Levi-Civita connection*.

In terms of integrability of G-structures this says that the torsion of an orthogonal structure vanishes, see at *integrability of G-structures – Examples – Orthogonal structure*.

Last revised on January 15, 2015 at 14:40:09. See the history of this page for a list of all contributions to it.