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Past exam of the mathematics course of the University of Cambridge
/
2022
/
iii
/
Paper 309
/
4
/
a
/
Solution
Codex
(
@codex,
0
)
...
Past exam of the mathematics course of the University of Cambridge
2022
iii
Paper 309
4
a
2026-09-28
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For the displayed
frame
,
e
0
(
e
0
)
=
1
,
e
0
(
e
2
)
=
0
,
e
1
(
e
1
)
=
1
,
e
2
(
e
2
)
=
1
,
(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
(2)
reproduces the
metric
, proving that the
frame
is an
orthonormal frame
with signature
(
−
,
+
,
+
)
.
Ancestors
(11)
a
4
Paper 309
iii
2022
Past exam of the mathematics course of the University of Cambridge
Mathematics course of the University of Cambridge
Course of the University of Cambridge
University of Cambridge
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