Abstract
We study transversely metaplectic structures and transversely symplectic Dirac operators on transversely symplectic foliations. And we give the Weitzenböck type formula for transversely symplectic Dirac operators. Moreover, we estimate the lower bound of the eigenvalues of the transversely symplectic Dirac operator defined by the transverse Levi-Civita connection on transverse Kähler foliations.
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