Calculate the connection one-forms, curvature two-forms, and hence the components of the Riemann tensor for the Mixmaster universe. The metric is given by
ds2 = −dt
dt + 21
1 + 22
Here , , and
are functions of t only, and the one-forms i are given by
1 = cos d + sin sin d,
2 = sin d − cos sin d,
3 = d + cos d.
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