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arXiv · 2208.13148

Compact leaves of the foliation defined by the kernel of a $T^2$-invariant presymplectic form

Asuka Hagiwara
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Abstract

We investigate the foliation defined by the kernel of an exact presymplectic form $d\alpha$ 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 $d\alpha$ and satisfies that the function $\alpha(Z_2)$ is constant, where $Z_1$, $Z_2$ are the infinitesimal generators of the $T^2$-action. We also give its generalization for r $\geq$ 1.

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Asuka Hagiwara. 2022-08-28. Compact leaves of the foliation defined by the kernel of a $T^2$-invariant presymplectic form. https://arxiv.org/abs/2208.13148

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