A Discrete Extrinsic and Intrinsic Dirac Operator. Issue 3 (31st August 2022)

• Record Type: Journal Article
• Authors: Hoffmann, Tim; Ye, Zi
• Is Part Of: Experimental mathematics. Volume 31:Issue 3(2022)
• Page Start: 920
• Page End: 935
• Publication Date: 2022-08-31
• Subjects: Discrete differential geometry -- spin geometry -- surface theory; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2020.1727798
• Languages: English
• ISSNs: 1058-6458

Abstract

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.