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The Moutard transformation of two-dimensional Dirac operators and Möbius geometry

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Abstract

We describe the action of inversion on given Weierstrass representations for surfaces and show that the Moutard transformation of two-dimensional Dirac operators maps the potential (the Weierstrass representation) of a surface S to the potential of a surface \(\tilde S\) obtained from S by inversion.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia

    I. A. Taimanov

  2. Novosibirsk State University, Novosibirsk, Russia

    I. A. Taimanov

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  1. I. A. Taimanov
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Correspondence to I. A. Taimanov.

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Original Russian Text © I. A. Taimanov, 2015, published in Matematicheskie Zametki, 2015, Vol. 97, No. 1, pp. 129–141.

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Taimanov, I.A. The Moutard transformation of two-dimensional Dirac operators and Möbius geometry. Math Notes 97, 124–135 (2015). https://doi.org/10.1134/S0001434615010149

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  • DOI: https://doi.org/10.1134/S0001434615010149

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