On the spinor representation of surfaces in Euclidean 3-space

1997/12/30 by Thomas Friedrich · 4 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Geometric Analysis and Curvature Flows #dg-ga #math.DG

paper · pdf · doi:10.1016/s0393-0440(98)00018-7

published as J.Geom.Phys. 28 (1998) 143-157 · 16 pages, LaTeX2.09

arxiv created 1997/12/30 · openalex publication_date 1998/11/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04

Abstract

The aim of the present paper is to clarify the relationship between immersions of surfaces and solutions of the inhomogeneous Dirac equation. The main idea leading to the description of a surface M² by a spinor field is the observation that the restriction to M² of any parallel spinor phi on R³ is (with respect to the inner geometry of M²) a non-trivial spinor field on M² of constant length which is a solution of the inhomogeneous Dirac equation and vice versa.

Cited by

• Upper bounds for the first eigenvalue of the Dirac operator on surfaces
• On Conservation Laws for the Supersymmetric Sigma Model
• Energy–momentum tensor on foliations
• Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds