I. A. Taimanov, “The Moutard Transformation of Two-Dimensional Dirac Operators and Möbius Geometry”, Mat. Zametki, 2015, Volume 97, Issue 1,Pages <nobr>129

This article is cited in 15 papers

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

I. A. Taimanov^ab

^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.

UDC: 514.76+517.95

Received: 06.08.2014

DOI: 10.4213/mzm10572