Abstract
The aim of the present paper is to clarify the relationship between immersions of surfaces and solutions of the 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 Ψ on R 2 is a non-trivial spinor field on M 2 of constant length which is a solution of the inhomogeneous Dirac equation. Vice versa, any solution of the equation D( Ψ) = H · Ψ of constant length defines a symmetric endomorphism satisfying the Gauss-and Codazzi equations, i.e. an isometric immersion of M 2 into the 3-dimensional Euclidean space.
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