- Fermi coordinates
In the mathematical theory of
Riemannian geometry , Fermi coordinates are local coordinates that are adapted to ageodesic .More formally, suppose "M" is an "n"-dimensional
Riemannian manifold , gamma is a geodesic on M, and p is a point on gamma. Then there exists local coordinates t,x^2, ldots, x^n)around p such that:
* For small "t", t,0,ldots, 0) represents the geodesic near p,
* On gamma, the metric tensor is the Euclidean metric,
* On gamma, allChristoffel symbol s vanish.Such coordinates are called Fermi coordinates and are named after the Italian physicist
Enrico Fermi . It should be emphasized that the above properties are only valid on the geodesic. For example, if all Christoffel symbols vanish near p, then the manifold is flat near p.ee also
*
Geodesic normal coordinates
*Christoffel symbols
*Isothermal coordinates
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