We investigate the foliation defined by the kernel of an exact presymplectic form dα of rank 2n on a (2n + 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(Z2) is constant, where Z1, Z2 are the infinitesimal generators of the T 2 -action. We also give its generalization for r ≥ 1.
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