Helicoids and axially symmetric minimal surfaces in 3-dimensional homogeneous spaces
Helicoids and axially symmetric minimal surfaces in 3-dimensional homogeneous spaces
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发表时间：
2007
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通讯作者：
M. Bekkar;F. Bouziani;Y. Boukhatem;J. Inoguchi
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作者：
M. Bekkar;F. Bouziani;Y. Boukhatem;J. Inoguchi
Bianchi-Cartan-Vranceanu空间是黎曼3-流形，其等距群至少有4维且不具有常负曲率。本文研究Bianchi-Cartan-Vranceanu空间中的螺旋面和轴对称极小曲面。特别是，轴对称极小曲面显式分类的椭圆函数。证明了不可约Bianchi-Cartan-Vranceanu空间中不存在全脐曲面。
The Bianchi-Cartan-Vranceanu spaces are Riemannian 3-manifolds whose isometry groups have at least 4-dimension and not of constant neg- ative curvature. In this paper we study helicoids and axially symmetric minimal surfaces in the Bianchi-Cartan-Vranceanu spaces. In particular, axially symmetric minimal surfaces are explicitly classifled in terms of el- liptic functions. Moreover the non-existence of totally umbilical surfaces in the irreducible Bianchi-Cartan-Vranceanu spaces is proved.