# Torsion form

The covariant differential of the vector-valued $1$-form of the displacement of an affine connection, the $2$-form $$\Omega = D \omega = d \omega + \theta \wedge \omega$$ where $\theta$ is the connection form. The torsion form satisfies the first Bianchi identity: $$d \Omega = \theta \wedge \Omega + \omega \wedge \Theta$$ where $\Theta$ is the curvature form of the given connection. The definition of a torsion form for reductive connections is analogous.