= Normal orthonormal frame
{title2=$\nabla_{E_i}E_j(p)=0$}
At any point of a <Riemannian manifold>, choose <geodesic normal coordinates> and orthonormalize their coordinate fields smoothly. At the point, the metric is the identity and its first derivatives vanish, so the orthonormalization coefficients have zero first derivatives. The <Christoffel symbols> also vanish there. This gives a local <Riemannian orthonormal frame> with the displayed property, useful for invariant identities evaluated at one point.
Back to article page
