Let $M$ a flat torsion free four dimensional manifold and let $t$ be a real function on it.
Define $$S_p=\{q\in M: t(p)=t(q)\}$$
than we can show that $S_p$ is a flat 3 dimensional manifold.
Now given a moving frame $e_\mu$ in $M$ such that $De_0=0$, where $D$ is a covariant derivative , define
$$\Gamma^{\rho}_{\mu \nu}=\theta^\rho(D_{e_\mu}e_\nu)$$
where $\theta^\rho $ is the dual moving frame
Now suppose that $e_j \in TS_p$ for $j=1,2,3$, how can we proof that $$\Gamma^{k}_{i j}=0$$
for $k,i,j=1,2,3$ ?