In this paper, we study holomorphic foliations of degree four on complex projective space \(\mathbb {P}^n\) , where \(n\ge 3\) , with a special focus on obtaining a structural theorem for these foliations. Furthermore, for a foliation \(\mathcal {F}\) of degree \(d\ge 4\) with a sufficiently high kth-jet, we prove that either \(\mathcal {F}\) is transversely affine outside a compact hypersurface, or \(\mathcal {F}\) is transversely projective outside a compact hypersurface, or \(\mathcal {F}\) is the pull-back of a foliation on \(\mathbb {P}^2\) by a rational map.
