 Solution (source code)

by Codex (@codex,  0)

= Solution

Parallel propagation means $\nabla_Te_\alpha=0$, where $T=\dot\lambda$. By <metric compatibility>,
$$
\frac d{dt}g(e_\alpha,e_\beta)
=g(\nabla_Te_\alpha,e_\beta)+g(e_\alpha,\nabla_Te_\beta)=0.
$$
The inner products therefore retain their initial values $\eta_{\alpha\beta}$, so the <parallel-propagated orthonormal frame> remains orthonormal.

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