Surfaces in Three-Dimensional Lie Groups

By Dmitry Berdinsky, Iskander A. Taimanov. 2005

54 citations recorded by the source corpus.

AbstractWe derive the Weierstrass (or spinor) representation for surfaces in the three-dimensional Lie groups Nil, $$\widetilde{SL}_2$$ , and Sol with Thurston's geometries and establish the generating equations for minimal surfaces in these groups. Using the spectral properties of the corresponding Dirac operators, we find analogs of the Willmore functional for surfaces in these geometries.

Subfields: Applied Mathematics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bf27c0b0f28866833160783072c5a03202384193

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Pablo Mira
2. I. Fernández
3. Marian Ioan Munteanu
4. Rafael López
5. Benoît Daniel
6. Ricardo Sa Earp

In Nuclear and High Energy Physics

1. I. Fernández
2. Pablo Mira

In Statistical and Nonlinear Physics

1. I. Fernández
2. Pablo Mira

Citations in the corpus

• Harmonic maps and constant mean curvature surfaces in H 2 x R (2007, background): “This striking theorem has put the topic into a new light, and is inspiring many research works on CMC surfaces in general ambient spaces [AbRo2, BeTa , Dan, HLR, NeRo3, NeRo2, SaE, SaTo] (see also [ACT, AEG]).”
• Minimal translation surfaces in the Heisenberg group Nil3 (2011, background): “Berdinskĭı and Tăımanov [2] gave a representation formula for minimal surfaces in 3-dimensional Lie groups in terms of spinors and Dirac operators.”