Dirac eigenvalues estimates in terms of symmetric tensors

TL;DR

This paper reviews recent advances in estimating lower eigenvalues of the Dirac operator, demonstrating improvements over Friedrich's inequality through symmetric tensors and applying these results to Sasakian spin manifolds.

Contribution

It introduces improved eigenvalue estimates for the Dirac operator using symmetric tensors and applies these to specific geometric structures.

Findings

Enhanced lower bounds for Dirac eigenvalues

Application to Sasakian spin manifolds

Improved inequalities over Friedrich's original estimate

Abstract

We review some recent results concerning lower eigenvalues estimates for the Dirac operator [6, 7]. We show that Friedrich's inequality can be improved via certain well-chosen symmetric tensors and provide an application to Sasakian spin manifolds.