Abstract

In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavor (that comes with spin transformations to comformally transfrom immersions) and the two are naturally related. In this paper we consider a corresponding pair of discrete Dirac operators, the latter on discrete surfaces with polygonal faces and normals defined on each face, and show that many key properties of the smooth theory are preserved. In particular, the corresponding spin transformations, conformal invariants for them, and the relation between this operator and its intrinsic counterpart are discussed.

摘要

在表面的微分几何中，狄拉克算子本质上表现为一种解决浸入问题的工具，以及一种外在的风格（伴随着自旋变换以从浸入式转换），两者自然相关。在本文中，我们考虑了一对相应的离散狄拉克算子，后者在离散表面上具有多边形面和在每个面上定义的法线，并表明保留了光滑理论的许多关键属性。特别地，讨论了相应的自旋变换、它们的共形不变量，以及该算子与其固有对应物之间的关系。