Transversely symplectic Dirac operators on a transversely symplectic foliation

TL;DR

This paper investigates the properties of transversely symplectic Dirac operators on foliations with symplectic structures, deriving formulas and eigenvalue bounds relevant to geometric analysis.

Contribution

It introduces the transversely metaplectic structure and derives a Weitzenbock formula for the transversely symplectic Dirac operator, along with eigenvalue estimates.

Findings

Derived a Weitzenbock type formula for the operator

Estimated eigenvalue lower bounds on transverse Kähler foliations

Analyzed the operator on special spinor spaces

Abstract

We study the transversely metaplectic structure and the transversely symplectic Dirac operator on a transversely symplectic foliation. Moreover, we give the Weitzenbock type formula for transversely symplectic Dirac operators and we estimate the lower bound of the eigenvalues of the transversely symplectic Dirac operator on special spinors space on transverse Kahler foliations.