A note on Mitsumatsu's construction of a leafwise symplectic foliation

Abstract

Mitsumatsu constructed leafwise symplectic structures of certain codimension one foliations of the 5-sphere. This inspired the present author to improve his result on convergence of contact structure to foliation. We describe convergence of contact strcture to leafwise symplectic foliation by means of confoliation equipped with a certain 2-form. Such a 2-form appears in the works of Nunes da Costa and Petalidou on twisted Jacobi structures and partially relates to weak domination due to Massot, Niederkruger and Wendl. We also construct leafwise symplectic foliations on the product of the 4-sphere and the circle.