Show that in the hyperbolic space $H^n\subset \mathbb{R}^{n+1}$ has constant curvature equal to -1.
DOUBT: How can I resolve this using only differential forms language?
PS: If $n=2$ then I would find a parametrization and apply $d\omega_{12}=-K\omega_1\wedge \omega_2$ after calculating coframe and connection forms. However with the power, $n$ is more difficult, and I couldn't think of a solution.