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An accelerated observer (both in curved or non-curved space) who Fermi Walker transports his own basis vectors set along his world line will have the metric in the minkowsky form [itex]\eta_{\mu\nu}[/itex] at

*each*point of the world line?

AND if the observer follows a geodesic, the condition of parallel transport [itex]\nabla_{U} V[/itex] along th geodesic is sufficient to keep the metric in the minkiwsky form at each point of the geodesic itself?

Thanks!