2017/09/06 by Xiu Ji, Ji, Xiu, Tongzhu Li +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1709.01657
openalex publication_date 2017/09/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study generic conformally flat hypersurfaces in the Euclidean 4-space ℝ4 using the framework of Möbius geometry. First, we classify locally the generic conformally flat hypersurfaces with closed Möbius form under the Möbius transformation group of ℝ4. Such examples come from cones, cylinders, or rotational hypersurfaces over the surfaces with constant Gaussian curvature in 3-spheres, Euclidean 3-spaces, or hyperbolic 3-spaces, respectively. Second, we investigate the global behavior of the generic conformally flat hypersurface and give some integral formulas about these hypersurfaces.