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 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 4 .

Shigeki Matsutani

Balkan Journal of Geometry and its Applications

BJGA是国际双年刊。 BJGA 涵盖了广泛的微分几何研究论文及其使用微分几何方法和研究几何结构的所有数学跨学科领域。涵盖以下主要领域：局部和全局微分几何、流形拓扑、李群、ODE 和 PDE流形、全局分析、流形优化和数学物理。

The Balkan Journal of Geometry and its Applications (BJGA) is an international biannual journal that covers a wide range of research in differential geometry and its applications across various interdisciplinary fields of mathematics. The main areas include local and global differential geometry, manifold topology, Lie groups, ordinary differential equations (ODE) and partial differential equations (PDE) on manifolds, global analysis, manifold optimization, and mathematical physics.

《Balkan Journal of Geometry and its Applications》（BJGA）是一本国际双年刊，涵盖了广泛的微分几何研究及其在各个数学跨学科领域中的应用。主要领域包括局部和全局微分几何、流形拓扑、李群、常微分方程（ODE）和偏微分方程（PDE）流形、全局分析、流形优化以及数学物理等。

Submanifold Dirac operators with torsion

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