[Topology and Geometry Seminar] “Conformally flat hypersurfaces and Guichard nets” by Dr Gudrun Szewieczek

The Topology and Geometry Seminar aims to introduce current mathematical research topics starting from the very basics. Anyone interested in mathematics is welcome to attend.

This week, Dr Gudrun Szewieczek (Technische Universität Wien/Kobe University) will give a talk on “Conformally flat hypersurfaces and Guichard nets”. Dr Szewieczek is co-hosted by the Fried and Tsvietkova Units.

Abstract: 100 years ago Cartan first posed the question to find a geometric characterization of conformally flat hypersurfaces. In this talk we give an overview on recent developments towards a geometric classification of these submanifolds using Guichard nets, particular curvature line coordinates. Viewed as triply orthogonal systems in R³ , these coordinate systems can be characterized by the existence of special associated systems.