Curvature of a distribution

We define the curvature of the distribution as the $R$ -bilinear skew-symmetric map

ω : Γ (D) \times Γ (D) \to Γ (\tilde{V})

ω (X, Y) := θ ([X, Y]) = [X, Y] mod Γ (D)

where $θ$ is the structure 1-form of the distribution.
Indeed, $ω$ is $C^{\infty} (M)$ -linear, so it comes from a bundle map

ω : Λ^{2} M \to \tilde{V}

([Vitagliano 2017] exercise 3.6)

When $ω = 0$ we have that $D$ is involutive distribution. If it has full rank it is called completely non-integrable.