Zero sets of eigenspinors for generic metrics

TL;DR

This paper proves that for generic metrics on certain 2- or 3-dimensional spin manifolds, eigenspinors of the Dirac operator are almost everywhere non-zero, using transversality and unique continuation principles.

Contribution

It establishes a generic property of eigenspinors being nowhere zero for Dirac operators on 2- and 3-dimensional spin manifolds, extending understanding of their zero sets.

Findings

Eigenspinors are nowhere zero for generic metrics

Uses transversality theorem and unique continuation property

Results apply to 2- and 3-dimensional spin manifolds

Abstract

Let $M$ be a closed connected spin manifold of dimension $2$ or $3$ with a fixed orientation and a fixed spin structure. We prove that for a generic Riemannian metric on $M$ the non-harmonic eigenspinors of the Dirac operator are nowhere zero. The proof is based on a transversality theorem and the unique continuation property of the Dirac operator.