The Global Property of Generic Conformally Flat Hypersurfaces in R⁴

A conformally flat hypersurface (Formula presented.) in the four-dimensional Euclidean space (Formula presented.) is said to be generic if the hypersurface has three distinct principal curvatures everywhere. In this paper, we study the generic conformally flat hypersurfaces in (Formula presented.) using the framework of Möbius geometry. First, we classify locally the generic conformally flat hypersurfaces with a vanishing Möbius form under the Möbius transformation group of (Formula presented.). Second, we investigate the global behavior of the compact generic conformally flat hypersurfaces and give some integral formulas about the Möbius invariant of these hypersurfaces.