Beitr\"age zur Algebra und Geometrie
Contributions to Algebra and Geometry
Volume 35 (1994), No. 2, 315-331.

On Conformally Flat Hypersurfaces and Guichard's Nets

U. Hertrich-Jeromin

Abstract

A local classification result for conformally flat hypersurfaces in a four
dimensional space form is obtained: they are characterized by the existence
of special principal curvature coordinates. By means of conformal coordinate
charts these coordinates are related to (conformal classes of) Guichard
nets in Euclidean three space which reflect some geometric properties of
the conformally flat hypersurface.