Conformally flat hypersurfaces with Bianchi-type Guichard net

Udo Hertrich-Jeromin, Yoshihiko Suyama

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 languageEnglish
Pages (from-to)1-30
Number of pages30
JournalOsaka Journal of Mathematics
Volume50
Issue number1
Publication statusPublished - Mar 2013

Fingerprint Dive into the research topics of 'Conformally flat hypersurfaces with Bianchi-type Guichard net'. Together they form a unique fingerprint.

  • Cite this

    Hertrich-Jeromin, U., & Suyama, Y. (2013). Conformally flat hypersurfaces with Bianchi-type Guichard net. Osaka Journal of Mathematics, 50(1), 1-30.