(adsbygoogle = window.adsbygoogle || []).push({}); Why Cant I Calculate 1-forms!?

Ive been given the following formula to find 1-forms:

[tex]2\omega_{ab} = e^d i(X_a)i(X_b)\mbox{d}e_d + i(X_b)\mbox{d}e_a - i(X_a)\mbox{d}e_b[/tex]

and have been asked to find all connection 1-forms. Of course, you cant find these 1-forms without a metric, so here it is:

[tex]g = -\mbox{d}t\otimes\mbox{d}t + f(t)^2\hat{g}[/tex]

where [itex]\hat{g}[/itex] is the metric on some 3-dimensional space of constant curvature c. My orthonormal frame is

[tex]e^0 = \mbox{d}t \quad \quad e^i = f(t)\hat{e}^i[/tex]

where [itex]\hat{e}^i[/itex] is a [itex]\hat{g}[/itex]-orthonormal frame. And note that [itex]X_i = \frac{1}{f}\hat{X}_i[/itex]. Phew! Hope thats not too hard to comprehend.

But I dont know what to put in for d in the index of e. Im aware that you have to sum over d but Im not sure what to sum over. 0,1,2,3? EDIT: Yes, I sum over everything.

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# Homework Help: Why Cant I Calculate 1-forms?

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