# The Dirac operator on locally reducible Riemannian manifolds

## TL;DR

This paper derives sharp estimates for higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, relating them to Laplace-Beltrami eigenvalues and scalar curvature, extending known results for the first eigenvalue.

## Contribution

It provides new sharp eigenvalue estimates for the Dirac operator on locally reducible manifolds, generalizing previous results for the first eigenvalue.

## Key findings

- Sharp bounds for higher Dirac eigenvalues
- Reduction to Alexandrov's result for the first eigenvalue
- Relations between Dirac eigenvalues, Laplace-Beltrami eigenvalues, and scalar curvature

## Abstract

In this paper, we get estimates on the higher eigenvalues of the Dirac operator on locally reducible Riemannian manifolds, in terms of the eigenvalues of the Laplace-Beltrami operator and the scalar curvature. These estimates are sharp, in the sense that, for the first eigenvalue, they reduce to the result of Alexandrov.