Extrinsic eigenvalue estimates for Dirac operator

TL;DR

This paper establishes bounds on the eigenvalues of Dirac operators for submanifolds, relating them to conformal and extrinsic geometric quantities of the ambient space.

Contribution

It provides new lower and upper eigenvalue bounds for Dirac operators based on extrinsic and conformal geometric data.

Findings

Derived bounds for Dirac eigenvalues in specific ambient manifolds.

Connected eigenvalue estimates to extrinsic geometric quantities.

Extended previous results to broader classes of submanifolds.

Abstract

In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.