We explain the construction of a smooth codimension-one foliation on the 5-sphere in which every leaf is a symplectic four-manifold and such that the symplectic structure varies smoothly. The construction implies the existence of a complete regular Poisson structure on the five-sphere. Apart from some spheres which can be foliated by Riemann surfaces (this foliations are orientable and therefore symplectic) this example provides the only example of a regular Poisson structure on a sphere. This is joint work with Pablo Suarez (CIMAT, Mexico).
A symplectic foliation of the 5-sphere
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