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arXiv · 1610.00561

The Moutard transformation of two-dimensional Dirac operators and conformal geometry of surfaces in the four-space

R. M. Matuev·I. A. Taimanov
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Abstract

The Moutard transformation for a two-dimensional Dirac operator with a complex-valued potential is constructed. It is showed that this transformation relates the potentials of Weierstrass representations of surfaces related by a composition of the inversion and a reflection with respect to an axis. It is given an analytical description of an explicit example of such a transformation which results in a creation of double points on the spectral curve of a Dirac operator with a double-periodic potential.

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R. M. Matuev, I. A. Taimanov. 2016-10-03. The Moutard transformation of two-dimensional Dirac operators and conformal geometry of surfaces in the four-space. https://arxiv.org/abs/1610.00561

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