Ribaucour Transformations for Hypersurfaces in Space Forms
Ribaucour Transformations for Hypersurfaces in Space Forms
复制标题
空间形式超曲面的 Ribaucour 变换
DOI：
10.1007/s10455-005-9010-8
复制
发表时间：
2006
影响因子：
0.7
通讯作者：
Qiaoling Wang
中科院分区：
文献类型：
--
作者：
K. Tenenblat;Qiaoling Wang
建立了空间形式中超曲面的Ribaucour变换理论。对于任何这样的超曲面M，它允许正交正规主向量场，它被证明存在一个全脐超曲面局部关联到M的一个Ribaucour变换。提供了一种在三维空间形式中获得线性温加滕曲面的方法。应用该理论，得到了单位球面上局部对应于平坦环面的一类新的单参数完备常平均曲率曲面族。该族包含一类球面上的完备CMC柱。特别地，人们得到一个家庭的完整的极小曲面和极小柱，局部相关的克利福德环面。
The theory of Ribaucour transformations for hypersurfaces in space forms is established. For any such hypersurfaceM, that admits orthonormal principal vector fields, it was shown the existence of a totally umbilic hypersurface locally associated toMby a Ribaucour transformation. A method of obtaining linear Weingarten surfaces in a three-dimensional space form is provided. By applying the theory, a new one-parameter family of complete constant mean curvature (cmc) surfaces in the unit sphere, locally associated to the flat torus, is obtained. The family contains a class of complete cmc cylinders in the sphere. In particular, one gets a family of complete minimal surfaces and minimal cylinders, locally associated to the Clifford torus.