Surfaces in three-dimensional Lie groups

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We derive the Weierstrass (or spinor) representation for surfaces in three-dimensional Lie groups Nil, \tilde{SL}_2, 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.
20 pages, some references added

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Differential Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/101167

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0503707
 http://arxiv.org/abs/math/0503707
 Siberian Mathematical Journal 46 (2005), 1005-1019

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arXiv