Eigenvalues of the basic Dirac operator on quaternion-Kahler foliations

TL;DR

This paper establishes an optimal lower bound for the eigenvalues of the basic Dirac operator on quaternion-Kahler foliations, characterizing the case of equality through quaternion-Kahler Killing spinors and providing illustrative examples.

Contribution

It introduces a new optimal eigenvalue bound for the basic Dirac operator on quaternion-Kahler foliations and characterizes the limiting case using Killing spinors.

Findings

Established an optimal lower bound for eigenvalues.

Characterized the limiting case via quaternion-Kahler Killing spinors.

Provided examples illustrating the theoretical results.

Abstract

In this paper, we give an optimal lower bound for the eigenvalues of the basic Dirac operator on a quaternion-Kahler foliation. The limiting case is characterized by the existence of quaternion-Kahler Killing spinors. We end this paper by giving some examples.