Tetrad formalism for the mixmaster universe:

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

2 +

23

3.

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.

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

2 +

23

3.

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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