Eigenvalues Estimates For The Dirac Operator In Terms Of Codazzi Tensors

TL;DR

This paper establishes a new lower bound for the first eigenvalue of the Dirac operator on compact Riemannian spin manifolds, incorporating scalar curvature and Codazzi tensors, extending classical estimates.

Contribution

It introduces a generalized eigenvalue estimate involving Codazzi tensors, broadening the scope of classical bounds for the Dirac operator.

Findings

Derived a lower bound depending on scalar curvature and Codazzi tensor

Generalized classical eigenvalue estimates for the Dirac operator

Applicable to compact Riemannian spin manifolds

Abstract

We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2].