Solution
= Solution
One has
$$
de^0=0,\qquad
de^i=\frac{p_i}{t}e^0\wedge e^i.
$$
Cartan's torsion-free first structure equation and metric compatibility give the only nonzero <connection 1-forms>:
$$
\boxed{\omega^i{}_0=\omega^0{}_i=\frac{p_i}{t}e^i},
\qquad
\omega^i{}_j=0\quad(i\neq j).
$$