2017/04/15 by Rafael Novais, Novais, Rafael, João Paulo dos Santos +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1704.04702
openalex publication_date 2017/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, geometric characterizations of conformally flat and radially\nflat hypersurfaces in mathbbSn \× \ℝ and \ℍn \×\n\ℝ are given by means of their extrinsic geometry. Under suitable\nconditions on the shape operator, we classify conformally flat hypersurfaces in\nterms of rotation hypersurfaces. In addition, a close relation between radially\nflat hypersurfaces and semi-parallel hypersurfaces is established. These\nresults lead to geometric descriptions of hypersurfaces with special intrinsic\nstructures, such as Einstein metrics, Ricci solitons and hypersurfaces with\nconstant scalar curvature.\n