Surfaces in three-dimensional Lie groups

Details Surfaces in three-dimensional Lie groups Surfaces in three-dimensional Lie groups

2005-03-30

arxiv.org/abs/math/0503707v2

Siberian Mathematical Journal 46 (2005), 1005-1019

Mathematics

Differential Geometry

20 pages, some references added

Scientific paper

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.

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