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>:
$$
\boxed{\omega^i{}_0=\omega^0{}_i=\frac{p_i}{t}e^i},
\qquad
\omega^i{}_j=0\quad(i\neq j).
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2021 / iii / Paper 309 / 3 / c / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2021/iii/paper-309/3/c/solution