# Fermi coordinates

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In the mathematical theory of Riemannian geometry, **Fermi coordinates** are local coordinates that are adapted to a geodesic.^{[1]}

More formally, suppose *M* is an *n*-dimensional Riemannian manifold, is a geodesic on , and is a point on . Then there exists local coordinates
around such that:

- For small
*t*, represents the geodesic near , - On , the metric tensor is the Euclidean metric,
- On , all Christoffel symbols vanish.

Such coordinates are called **Fermi coordinates** and are named after the Italian physicist Enrico N. Fermi. The above properties are only valid on the geodesic. For example, if all Christoffel symbols vanish near , then the manifold is flat near .