We have constructed a leafwise symplectic structure for a foliation on the 5 sphere which is associated to the Milnor fibration of a simple elliptic hypersurface singularity in 3 complex variables. The foliation associated with $x^3+y^3+z^3=0$ is nothing but Lawson’s foliation which was constructed as the 1^st codimension one foliation on the 5 sphere in 1970. In this talk we abstract the essence of the construction as a framework to produce a leafwise symplectic foliation or a family of almost contact structure converging to a symplectic foliation from an exact symplectic open book decomposition supporting a contact structure.

As a by-product of the framework, we can show that a similar construction works also for the cusp singularities in 3 variables. If the time allows we discuss about the possibility of further applicability of the framework as well as the impossibility.