Parallel translation

Question

I read that for the Lorentz metric defined as

$d(a,b,c,d)=-a^2+b^2+c^2+d^2$

in $R^4$ the parallel translation (corresponding to the Levi-Civita Connection of $d$) agrees with the parallel translation of $\mathbb{R}^{n+1}$.

Could someone explain why?

Answer 1

In $\mathbb{R}^4$, not in $\mathbb{R}^{n+1}$.

The reason is that this Lorentzian-metrics is flat : there is no curvature.