Eigenvalue estimate for the Dirac-Witten operator on locally reducible Riemannian manifolds

TL;DR

This paper derives optimal lower bounds for the eigenvalues of the Dirac-Witten operator on certain Riemannian manifolds, analyzing both intrinsic and extrinsic geometric factors and exploring limiting cases.

Contribution

It provides new optimal eigenvalue estimates for the Dirac-Witten operator on locally reducible Riemannian manifolds, including analysis of limiting cases.

Findings

Established optimal lower bounds for eigenvalues

Analyzed intrinsic and extrinsic geometric influences

Studied limiting cases of the bounds

Abstract

We get optimal lower bounds for the eigenvalues of the Dirac-Witten operator on locally reducible spacelike submanifold in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied.