Lower bounds of the Dirac eigenvalues on compact Riemannian spin manifolds with locally product structure

TL;DR

This paper establishes lower bounds for the eigenvalues of the Dirac operator on compact Riemannian spin manifolds with locally product structures, inspired by similarities with almost Hermitian structures, and provides examples for the limiting cases.

Contribution

It introduces new eigenvalue estimates for the Dirac operator on manifolds with locally product structures, expanding understanding of geometric analysis in this context.

Findings

Derived lower bounds for Dirac eigenvalues on such manifolds

Identified examples that achieve the limiting cases of these bounds

Connected almost product and almost Hermitian structures in spectral estimates

Abstract

We study some similarities between almost product Riemannian structures and almost Hermitian structures. Inspired by the similarities, we prove lower eigenvalue estimates for the Dirac operator on compact Riemannian spin manifolds with locally product structures. We also provide some examples (limiting manifolds) for the limiting case of the estimates.