A Discrete Extrinsic and Intrinsic Dirac Operator
A Discrete Extrinsic and Intrinsic Dirac Operator
复制标题
离散外本质狄拉克算子
DOI：
10.1080/10586458.2020.1727798
复制
发表时间：
2018
影响因子：
0.5
通讯作者：
Zi Ye
中科院分区：
文献类型：
--
作者：
T. Hoffmann;Zi Ye
摘要 在曲面的微分几何中，狄拉克算子本质上是作为解决浸没问题的工具，也是一种外在的风格（伴随着自旋变换到从浸没的共形变换），并且两者自然相关。在本文中，我们考虑一对相应的离散狄拉克算子，后者在具有多边形面和每个面上定义法线的离散表面上，并表明保留了平滑理论的许多关键属性。特别是，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内在对应物之间的关系。
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.