Let $\mathcal{F}$ be a foliation on a manifold $M$, and denote by $N\mathcal{F}$ its normal bundle. There is a flat $T\mathcal{F}$-connection on $N\mathcal{F}$, called Bott connection, given by $$ \nabla_{X}\overline{Y}:=\overline{[X,Y]}. $$ One gets a complex $(\Omega(\mathcal{F},N\mathcal{F}),d_{\nabla})$ consisting of leafwise differential forms on $\mathcal{F}$ with values in $N\mathcal{F}$. The cohomology group $H^{1}(\mathcal{F},N\mathcal{F})$ plays an important role in the deformation theory of $\mathcal{F}$, since it parametrizes infinitesimal deformations.
What are some examples of foliations $\mathcal{F}$ for which $H^{1}(\mathcal{F},N\mathcal{F})$ vanishes?
