Geodesic
The Moutard Transformation of Two-Dimensional Dirac Operators and M\"obius Geometry
Matematičeskie zametki, Tome 97 (2015) no. 1, pp. 129-141

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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 $\widetilde{S}$ obtained from $S$ by inversion.
Mots-clés : Moutard transformation, inversion, conformal immersion of a domain.
Keywords: two-dimensional Dirac operator, Möbius geometry, Weierstrass representation for surfaces 
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     author = {I. A. Taimanov},
     title = {The {Moutard} {Transformation} of {Two-Dimensional} {Dirac} {Operators} and {M\"obius} {Geometry}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {129--141},
     publisher = {mathdoc},
     volume = {97},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_1_a12/}
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I. A. Taimanov. The Moutard Transformation of Two-Dimensional Dirac Operators and M\"obius Geometry. Matematičeskie zametki, Tome 97 (2015) no. 1, pp. 129-141. http://geodesic.mathdoc.fr/item/MZM_2015_97_1_a12/