For the displayed frame,
$$
e^0(e_0)=1,
\quad e^0(e_2)=0,
\quad e^1(e_1)=1,
\quad e^2(e_2)=1,
$$
and all other pairings vanish. Hence the proposed one-forms are the dual coframe. Substitution into
$$
g=-(e^0)^2+(e^1)^2+(e^2)^2
$$
reproduces the metric, proving that the frame is an <orthonormal frame> with signature $(-,+,+)$.

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 309 / 4 / a / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-309/4/a/solution