View source for Fermi coordinates

Coordinates in which the components of the [[Metric tensor|metric tensor]] of a Riemannian space, computed along the points of some curve, are the same as the components of the metric tensor of a Euclidean space in Cartesian coordinates. The concept of Fermi coordinates can be generalized pseudo-Riemannian spaces, for which they were also first introduced by E. Fermi (1922) [[#References|[1]]]. He showed that in a neighbourhood of a sufficiently small segment of a sufficiently regular time-like curve on a sufficiently regular pseudo-Riemannian manifold of Lorentzian signature there actually are Fermi coordinates.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  E. Fermi,   "Sopra i fenomeni che avvengono in vinicinanza di una linea ovaria"  ''Atti R. Accad. Lincei Rend. Cl. Sci. Fis. Mat. Nat.'' , '''31'''  (1922)  pp. 21–51</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  P.K. [P.K. Rashevskii] Rashewski,   "Riemannsche Geometrie und Tensoranalyse" , Deutsch. Verlag Wissenschaft.  (1959)  (Translated from Russian)</TD></TR></table>



====Comments====
Using properties of the [[Exponential mapping|exponential mapping]] restricted to the normal bundle of a curve of fixed causal character and without self-intersections, the existence of Fermi coordinates along any compact piece of the curve can be shown in an arbitrary [[Pseudo-Riemannian space|pseudo-Riemannian space]].