论文标题
三个球的通用形式平坦的高空曲面和表面
Generic conformally flat hypersurfaces and surfaces in 3-sphere
论文作者
论文摘要
本文的目的是验证在4维空间形式中对通用的共形扁平曲面的研究降低为标准3-Sphere中的表面理论。通用共形平面（局部）超曲面的共形结构的特征是具有guichard条件的共形扁平（局部 - ）3分。然后，有一类具有恒定高斯曲率-1的正交分析（局部）Riemannian 2-Metrics-1，使得该类别的任何2米都会产生一个具有guichard条件的一组共形的3-Metrics。在本文中，我们首先将班级的两种学术关系与三个球体中的表面相关：对于班级的2米，在3个角度中，确定了一组5维的（非等法）分析表面，以确定该集合的任何层面，以至于从表面上构成了表面的任何表面，并从表面上构成了一定的表面，并且在近似地图中，YESSERFORTAIRS的表面是蜂巢的一部分。欧几里得4空间。其次，我们表征了三个球体中的分析表面，这会引起通用的纯种曲面。
The aim of this paper is to verify that the study of generic conformally flat hypersurfaces in 4-dimensional space forms is reduced to a surface theory in the standard 3-sphere. The conformal structure of generic conformally flat (local-)hypersurfaces is characterized as conformally flat (local-)3-metrics with the Guichard condition. Then, there is a certain class of orthogonal analytic (local-)Riemannian 2-metrics with constant Gauss curvature -1 such that any 2-metric of the class gives rise to a one-parameter family of conformally flat 3-metrics with the Guichard condition. In this paper, we firstly relate 2-metrics of the class to surfaces in the 3-sphere: for a 2-metric of the class, a 5-dimensional set of (non-isometric) analytic surfaces in the 3-sphere is determined such that any surface of the set gives rise to an evolution of surfaces in the 3-sphere issuing from the surface and the evolution is the Gauss map of a generic conformally flat hypersurface in the Euclidean 4-space. Secondly, we characterize analytic surfaces in the 3-sphere which give rise to generic conformally flat hypersurfaces.
