nLab
Riemann normal coordinates

Context

Riemannian geometry

Differential geometry

differential geometry

synthetic differential geometry

Axiomatics

Models

Concepts

Theorems

Applications

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).

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.

References

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