On conformally flat hypersurfaces, curved flats and cyclic systems
type: Item
instance of: scholarly article
title: On conformally flat hypersurfaces, curved flats and cyclic systems
zbMATH Open document ID: 0870.53007
DOI: 10.1007/BF02567966
published in: Manuscripta Mathematica
publication date: 1997-09-15T00:00:00Z
full work available at URL: https://eudml.org/doc/156241
review text: A Riemannian manifold \((M,g)\) is called conformally flat if the conformally equivalent metric \(e^{2u} g\) is flat for some appropriate function \(u\). The author characterizes conformally flat hypersurfaces in \(S^{n+1}\): they can be equipped with a normal congruence of circles having a whole 1-parameter family of conformally flat hypersurfaces which intersect the congruence orthogonally. The paper begins with brief introduction into Möbius geometry and involves interesting comments on the history (É. Cartan's results) and on the sense of the result (especially for the theory of curvature isotropic submanifolds).
Mathematics Subject Classification ID: 53A30
Mathematics Subject Classification ID: 53C40
zbMATH DE Number: 980723
zbMATH Keywords: conformal geometry
zbMATH Keywords: curved flatness
zbMATH Keywords: conformal flatness
zbMATH Keywords: conformally flat hypersurfaces
zbMATH Keywords: Möbius geometry
author: Udo Hertrich-Jeromin
reviewed by: Jan Chrastina
MaRDI profile type: Publication
cites work: Curved flats and isothermic surfaces
cites work: Q3897665
cites work: Q4885544
cites work: On conformally flat hypersurfaces and Guichard's nets
description: scientific article; zbMATH DE number 980723