nLab Riemann normal coordinates

Context

Riemannian geometry

Riemannian geometry

Applications

Differential geometry

differential geometry

synthetic differential geometry

Contents

Idea

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).

References

Created on September 10, 2012 02:10:56 by Urs Schreiber (82.113.99.41)