Transversal hard Lefschetz theorem on transversely symplectic foliations

TL;DR

This paper extends the transversal hard Lefschetz theorem to general transversely symplectic foliations, broadening the understanding of symplectic structures in foliation theory.

Contribution

It generalizes previous results on transversally symplectic flows to all transversely symplectic foliations.

Findings

Extended the transversal hard Lefschetz theorem to new classes of foliations

Connected symplectic foliation theory with harmonic theory

Provided new tools for studying transversely symplectic structures

Abstract

We study the transversal hard Lefschetz theorem on a transversely symplectic foliation. This article extends the results of transversally symplectic flows (H.K.~Pak, "Transversal harmonic theory for transversally symplectic flows", J. Aust. Math. Soc. 84 (2008), 233--245) to the general transversely symplectic foliation.