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Matematicheskie Zametki, 2015, Volume 97, Issue 1, Pages 129–141
DOI: https://doi.org/10.4213/mzm10572 (Mi mzm10572) 		 
This article is cited in 15 scientific papers (total in 15 papers)

The Moutard Transformation of Two-Dimensional Dirac Operators and Möbius Geometry

I. A. Taimanovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (527 kB) Citations (15)
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DOI: https://doi.org/10.4213/mzm10572
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 $\widetilde{S}$ obtained from $S$ by inversion.
Keywords: Moutard transformation, two-dimensional Dirac operator, Möbius geometry, inversion, Weierstrass representation for surfaces, conformal immersion of a domain.
Funding agency Grant number
Russian Science Foundation 14-11-00441
This work was supported by the Russian Science Foundation (grant no. 14-11-00441).
Received: 06.08.2014
English version:
Mathematical Notes, 2015, Volume 97, Issue 1, Pages 124–135
DOI: https://doi.org/10.1134/S0001434615010149
Bibliographic databases:
Document Type: Article
UDC: 514.76+517.95
Language: Russian
Citation: I. A. Taimanov, “The Moutard Transformation of Two-Dimensional Dirac Operators and Möbius Geometry”, Mat. Zametki, 97:1 (2015), 129–141; Math. Notes, 97:1 (2015), 124–135
Citation in format AMSBIB
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    • This publication is cited in the following 15 articles:
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