2018/02/17 by Tim Hoffmann, Zi Ye, Hoffmann, Tim +1
Computer Science · Engineering · Mathematics · #52C99 #53A05 #Advanced Mathematical Modeling in Engineering #Algebraic and Geometric Analysis #Composite Material Mechanics #Differential Geometry (math.DG) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1802.06278
openalex publication_date 2018/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In differential geometry of surfaces the Dirac operator appears intrinsically as a tool to address the immersion problem as well as in an extrinsic flavour (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.