Note on concentration via the conjugate-linear Hodge star operator

TL;DR

This paper introduces conjugate-linear perturbations of twisted spinc Dirac operators on certain compact manifolds, utilizing a rescaled conjugate-linear Hodge star operator, which satisfy the concentration principle.

Contribution

It constructs novel conjugate-linear perturbations of Dirac operators on almost hermitian manifolds using a rescaled conjugate-linear Hodge star operator.

Findings

Perturbations satisfy the concentration principle.

Construction applies to manifolds of dimension 2 or 6 mod 8.

Employs a rescaled conjugate-linear Hodge star operator.

Abstract

We construct conjugate-linear perturbations of twisted spinc Dirac operators on compact almost hermitian manifolds of dimension congruent to 2 or 6 modulo 8, employing the conjugate-linear Hodge star operator rescaled by unit complex numbers depending on degree. These perturbations satisfy the concentration principle.