Affine Deformation of Codimension‐One Foliation Pairs Into Engel Structures

In this paper, we study affine deformations of pairs of codimension‐one foliations into Engel structures on 4‐manifolds. Starting from a pair of defining Engel forms associated with such foliations, we introduce a deformation framework that preserves the Engel condition under suitable algebraic constraints. Within this setting, we establish criteria ensuring stability of the Engel condition under affine deformation and we analyze the induced compatibility with foliation pairs. As an application, we construct Engel structures on , where Σ is a closed hyperbolic surface, and we investigate geometric Engel structures modeled on Thurston four‐dimensional geometries, showing that specific cases can be realized via pairs of foliations.