Fermi coordinates

In the mathematical theory of Riemannian geometry, Fermi coordinates are local coordinates that are adapted to a geodesic.

More formally, suppose M is an n-dimensional Riemannian manifold, ${\displaystyle \gamma }$ is a geodesic on ${\displaystyle M}$, and ${\displaystyle p}$ is a point on ${\displaystyle \gamma }$. Then there exists local coordinates ${\displaystyle (t,x^{2},\ldots ,x^{n})}$ around ${\displaystyle p}$ such that:

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