Riemann normal coordinates

Around every point of a Riemannian manifold there is a coordinate system such that the Levi-Civita connection of the metric pulled back to these coordinates vanishes *at that point*. (Notice that the Riemann curvature will not in general vanish even at that point).

In the context of general relativity this reflects aspects of the equivalence princile (physics)?.

In the sense of integrability of G-structures, Riemann normal coordinates exhibit the first-order integrability of orthogonal structure, see at *integrability of G-structures – Examples – Orthogonal structure*.

- Wikipedia,
*Normal coordinates*

Revised on January 15, 2015 14:18:58
by Urs Schreiber
(89.204.135.3)