2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57380The 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 $\EE^4$.s16 pagesMathematical PhysicsDifferential Geometrytext