论文标题
dupin Hypersurfaces的分类中的几何形状
Classifications of Dupin Hypersurfaces in Lie Sphere Geometry
论文作者
论文摘要
这是对$ s^n $（或$ {\ bf r}^n $中的Dupin Hypersurfaces的本地和全球分类结果的调查，这些结果已在Lie Sphere几何形状的背景下获得。重点是将Dupin Hypersurfaces与球体中的等式曲面相关联的结果。除了这些分类结果外，详细描述了许多来自Lie Sphere几何形状的重要概念，例如曲率球，曲线和$ s^n $的子手机的Legendre Lifts（或$ {\ bf r}^n $）。该论文还包含具有某些特殊特性的Dupin Hypersurfaces的几种重要结构。
This is a survey of local and global classification results concerning Dupin hypersurfaces in $S^n$ (or ${\bf R}^n$) that have been obtained in the context of Lie sphere geometry. The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres. Along with these classification results, many important concepts from Lie sphere geometry, such as curvature spheres, Lie curvatures, and Legendre lifts of submanifolds of $S^n$ (or ${\bf R}^n$), are described in detail. The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.
