Connection 1-form
= Connection 1-form
{title2=$\omega^a{}_b$}
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Connection one-forms are defined by $\nabla e_b=\omega^a{}_b\otimes e_a$. For the Levi-Civita connection they obey Cartan's torsion-free equation $d\theta^a+\omega^a{}_b\wedge\theta^b=0$ and metric compatibility $\omega_{ab}=-\omega_{ba}$.