# 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)