On the Spinor Representation of Surfaces in Euclidean 3-Space

Details On the Spinor Representation of Surfaces in Euclidean 3-Space On the Spinor Representation of Surfaces in Euclidean 3-Space

1997-12-30

arxiv.org/abs/dg-ga/9712021v1

J.Geom.Phys. 28 (1998) 143-157

Mathematics

Differential Geometry

16 pages, LaTeX2.09

Scientific paper

10.1016/S0393-0440(98)00018-7

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 M^2 by a spinor field is the observation that the restriction to M^2 of any parallel spinor phi on R^3 is (with respect to the inner geometry of M^2) a non-trivial spinor field on M^2 of constant length which is a solution of the inhomogeneous Dirac equation and vice versa.

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