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Ali Taghavi
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Existence of compact leaf for certain foliation of a symplectic manifold

Is there a symplectic manifold $(M,\omega)$ equipped with a Riemannian metric such that $d^* \omega \wedge dd^*\omega=0$ and there is a compact leaf for the foliation of $M\setminus S$ defined by $d^* \omega =0$ where $S$ is the singular points of $d^* \omega$?(The opertor $d^*$ is the adjoint of the exterior derivative $d$).

In dimension $2$ the answer is negative since we lead to a gradient vector field which has no any closed orbit.

Ali Taghavi
  • 356
  • 8
  • 31
  • 123