An Extension of The Classical Ribaucour Transformation
An Extension of The Classical Ribaucour Transformation
复制标题
经典里包古变换的延伸
DOI：
10.1112/plms/85.1.211
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发表时间：
2002
影响因子：
1.8
通讯作者：
R. Tojeiro
中科院分区：
文献类型：
--
作者：
M. Dajczer;R. Tojeiro
我们将里鲍库尔变换的概念从经典表面理论扩展到具有任意维数和余维数的伪黎曼空间形式的完整子流形理论，即具有承认全局主坐标系的平坦法束的子流形。对于具有恒定均值或高斯曲率的曲面的里包古变换中是否存在具有相同性质的其他曲面的问题，比安奇给出了肯定的答案。我们的主要成就是解决了具有恒定截面曲率的完整子流形类的相同问题。
We extend the notion of Ribaucour transformation from classical surface theory to the theory of holonomic submanifolds of pseudo‐Riemannian space forms with arbitrary dimension and codimension, that is, submanifolds with flat normal bundle admitting a global system of principal coordinates. Bianchi gave a positive answer to the question of whether among the Ribaucour transforms of a surface with constant mean or Gaussian curvature there exist other surfaces with the same property. Our main achievement is to solve the same problem for the class of holonomic submanifolds with constant sectional curvature.