On the Spinor Representation of Surfaces in Euclidean 3-Space
Thomas Friedrich
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.
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