Compact leaves of the foliation defined by the kernel of a T2-invariant presymplectic form

Abstract

We investigate the foliation defined by the kernel of an exact presymplectic form dα of rank 2 n on a (2 n + r )-dimensional closed manifold M . For r = 2, we prove that the foliation has at least two leaves which are homeomorphic to a 2-dimensional torus, if M admits a locally free T 2 -action which preserves dα and satisfies that the function α ( Z 2 ) is constant, where Z 1 , Z 2 are the infinitesimal generators of the T 2 -action. We also give its generalization for r ≥ 1.