a = \frac{v}{2 r}, b = \frac{1}{r}, c = \frac{v}{r}, d = \frac{c o t θ}{r} .

Direct exterior differentiation gives

d e^{0} = 0, d e^{1} = a, e^{0} \land e^{1},

d e^{2} = b, e^{1} \land e^{2} - c, e^{0} \land e^{2},

d e^{3} = b, e^{1} \land e^{3} - c, e^{0} \land e^{3} + d, e^{2} \land e^{3} .

ω_{μν} = - ω_{νμ}

gives the independent mixed-index connection 1-forms

ω^{0}_{1} = a e^{1}, ω^{0}_{2} = - c e^{2}, ω^{0}_{3} = - c e^{3},

ω^{1}_{2} = - b e^{2}, ω^{1}_{3} = - b e^{3}, ω^{2}_{3} = - d e^{3} .

The remaining forms follow from Lorentz-signature antisymmetry:

ω^{1}_{0} = ω^{0}_{1}

ω^{2}_{0} = ω^{0}_{2}

ω^{3}_{0} = ω^{0}_{3}

, and

ω^{j}_{i} = - ω^{i}_{j}

for spatial indices.

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