Lower bounds for the eigenvalue estimates of the submanifold Dirac operator

TL;DR

This paper establishes optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds, linking intrinsic and extrinsic geometric quantities, and explores the limiting cases.

Contribution

It provides new optimal lower bounds for eigenvalues of the submanifold Dirac operator, extending and unifying several known results in the field.

Findings

Optimal lower bounds for eigenvalues derived

Limiting cases analyzed in detail

Connections made between intrinsic and extrinsic geometry

Abstract

We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, one gets several known results in this direction.