Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1-30 |
| Number of pages | 30 |
| Journal | Osaka Journal of Mathematics |
| Volume | 50 |
| Issue number | 1 |
| Publication status | Published - Mar 2013 |