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Mat. Zametki, 2015, Volume 97, Issue 1, Pages 129–141 (Mi mz10572)  

This article is cited in 8 scientific papers (total in 8 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

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).


DOI: https://doi.org/10.4213/mzm10572

Full text: PDF file (527 kB)
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English version:
Mathematical Notes, 2015, 97:1, 124–135

Bibliographic databases:

UDC: 514.76+517.95
Received: 06.08.2014

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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. A. Taimanov, “Blowing up solutions of the modified Novikov–Veselov equation and minimal surfaces”, Theoret. and Math. Phys., 182:2 (2015), 173–181  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    2. P. G. Grinevich, R. G. Novikov, “Generalized Analytic Functions, Moutard-Type Transforms, and Holomorphic Maps”, Funct. Anal. Appl., 50:2 (2016), 150–152  mathnet  crossref  crossref  mathscinet  isi  elib
    3. R. G. Novikov, I. A. Taimanov, “Moutard type transformation for matrix generalized analytic functions and gauge transformations”, Russian Math. Surveys, 71:5 (2016), 970–972  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. R. M. Matuev, I. A. Taimanov, “The Moutard Transformation of Two-Dimensional Dirac Operators and the Conformal Geometry of Surfaces in Four-Dimensional Space”, Math. Notes, 100:6 (2016), 835–846  mathnet  crossref  crossref  mathscinet  isi  elib
    5. Grinevich P.G., Novikov R.G., “Moutard Transform for Generalized Analytic Functions”, J. Geom. Anal., 26:4 (2016), 2984–2995  crossref  mathscinet  zmath  isi  scopus
    6. Grinevich P.G., Novikov R.G., “Moutard transform approach to generalized analytic functions with contour poles”, Bull. Sci. Math., 140:6 (2016), 638–656  crossref  mathscinet  zmath  isi  elib  scopus
    7. P. G. Grinevich, S. P. Novikov, “Singular solitons and spectral meromorphy”, Russian Math. Surveys, 72:6 (2017), 1083–1107  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    8. R. G. Novikov, I. A. Taimanov, “Darboux–Moutard transformations and Poincaré–Steklov operators”, Proc. Steklov Inst. Math., 302 (2018), 315–324  mathnet  crossref  crossref  isi  elib
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