Parallel frame along a curve
= Parallel frame along a curve
{title2=$D_tE_a=0$}
= Parallel frame
{synonym}
A parallel frame along a curve consists of a basis of <vector fields> $E_a$ satisfying $D_tE_a=0$ for its <covariant derivative along a curve>. Transporting a basis at the initial point constructs the frame. If the connection preserves the metric, an initially orthonormal basis stays orthonormal. In this frame the <Jacobi equation> becomes a linear matrix <ordinary differential equation>.