Submanifold Dirac Operator with Torsion

TL;DR

This paper introduces a new submanifold Dirac operator for surfaces in four-dimensional Euclidean space incorporating torsion via a U(1)-gauge field, linking geometric immersion data with Dirac operators.

Contribution

It defines a novel submanifold Dirac operator on surfaces in 4 with torsion modeled by a U(1)-gauge field, extending previous studies to include torsion effects.

Findings

New Dirac operator incorporating torsion in 4

Connection between immersion data and Dirac operator with torsion

Potential applications in geometric analysis and gauge theory

Abstract

The submanifold Dirac operator has been studied for this decade, which is closely related to Frenet-Serret and generalized Weierstrass relations. In this article, we will give a submanifold Dirac operator defined over a surface immersed in $\EE^4$ with U(1)-gauge field as torsion in the sense of the Frenet-Serret relation, which also has data of immersion of the surface in $\EE^4$.s