Surfaces in three-dimensional Lie groups

2005/03/31 by Dmitry A. Berdinsky, Iskander A. Taimanov · 1 citation
Mathematics · #math.DG

paper · pdf

published as Siberian Mathematical Journal 46 (2005), 1005-1019 · 20 pages, some references added

arxiv created 2005/11/14 · arxiv updated 2009/12/01

Abstract

We derive the Weierstrass (or spinor) representation for surfaces in three-dimensional Lie groups Nil, SL₂, and Sol with Thurston's geometries and establish the generating equations for minimal surfaces in these groups. By using the spectral properties of the corresponding Dirac operators we find analogs of the Willmore functional for surfaces in these geometries.

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• A duality for minimal surfaces in the Heisenberg group