Abstract
We use the concept of spinor operator to study some aspects of the classical theory of surfaces in three dimensions. We show that a spinor operator representing a surface satisfies a pair of Dirac-like equations and that this spinor operator representation is a generalization of the Weierstrass representation of minimal surfaces. We also obtain spinor operator representations of a surface directly from its parameterization in terms of isothermal parameters, without the need of solving the pair of Dirac-like equations. We apply these results to minimal surfaces and their deformations and also show how they can be written in terms of quaternions and complex numbers.
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