CONFORMALLY FLAT HYPERSURFACES WITH BIANCHI-TYPE GUICHARD NET
CONFORMALLY FLAT HYPERSURFACES WITH BIANCHI-TYPE GUICHARD NET
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DOI：
10.18910/24480
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发表时间：
2013-03
影响因子：
0.4
通讯作者：
U. Hertrich-Jeromin;Y. Suyama
中科院分区：
文献类型：
--
作者：
U. Hertrich-Jeromin;Y. Suyama
得到了共形球面中一般三维共形平坦超曲面的部分分类结果：得到了具有Bianci-型正则Guichard网的共形平坦超曲面的显式解析数据。这是第一个不附加对称性的共形平坦超曲面的分类结果。我们讨论了共形平坦超曲面的曲线平坦伴生族，并证明了它降为共形平坦超曲面的伴生族。研究了具有Bianci-型Guichard网的共形平坦超曲面族。
We obtain a partial classification result for generic $3$-dimensional conformally flat hypersurfaces in the conformal $4$-sphere: explicit analytic data are obtained for conformally flat hypersurfaces with Bianchi-type canonical Guichard net. This is the first classification result for conformally flat hypersurfaces without additional symmetry. We discuss the curved flat associated family for conformally flat hypersurfaces and show that it descends to an associated family of conformally flat hypersurfaces. The associated family of conformally flat hypersurfaces with Bianchi-type Guichard net is investigated.