2014/02/14 by Zhenxiao Xie, Tongzhu Li, Xiang Ma +2
Mathematics · #Conformal map #Curvature #Gaussian curvature #Geometric Analysis and Curvature Flows #Geometry #Ideal (ethics) #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Mathematics and Applications #Mean curvature #Point processes and geometric inequalities #Pure mathematics #Scalar curvature #Space form #Submanifold #math.DG #msc:53A30 #msc:53A55 #msc:53C42
paper · pdf · doi:10.1007/s11425-013-4664-3
21 pages
arxiv created 2014/02/14 · openalex publication_date 2014/04/10 · arxiv updated 2015/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Wintgen ideal submanifolds in space forms are those ones attaining equality at every point in the so-called DDVV inequality which relates the scalar curvature, the mean curvature and the normal scalar curvature. This property is conformal invariant; hence we study them in the framework of Moebius geometry, and restrict to three dimensional Wintgen ideal submanifolds in S5. In particular we give Moebius characterizations for minimal ones among them, which are also known as (3-dimensional) austere submanifolds (in 5-dimensional space forms).