Surfaces in three-dimensional Lie groups
微分几何
2007-05-23 v2
摘要
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.
引用
@article{arxiv.math/0503707,
title = {Surfaces in three-dimensional Lie groups},
author = {Dmitry A. Berdinsky and Iskander A. Taimanov},
journal= {arXiv preprint arXiv:math/0503707},
year = {2007}
}
备注
20 pages, some references added