Eigenvalue Estimates for the Dirac Operator on Quaternionic Kaehler Manifolds

TL;DR

This paper establishes a sharp lower bound for the eigenvalues of the Dirac operator on compact quaternionic Kähler manifolds, extending spectral estimates in geometric analysis.

Contribution

It provides the first eigenvalue estimate for the Dirac operator on quaternionic Kähler manifolds, with sharpness demonstrated on quaternionic projective space.

Findings

Derived a lower bound for the Dirac operator spectrum

Proved the estimate is sharp on quaternionic projective space

Extended spectral analysis to quaternionic Kähler geometry

Abstract

We consider the Dirac operator on compact quaternionic Kaehler manifolds and prove a lower bound for the spectrum. This estimate is sharp since it is the first eigenvalue of the Dirac operator on the quaternionic projective space.