On conformally flat hypersurfaces, curved flats and cyclic systems
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).
scientific article; zbMATH DE number 980723