2013/01/21 by Tongzhu Li, Xiang Ma, Li, Tongzhu +3 · 1 citation
Mathematics · #53A30 #53A55 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Point processes and geometric inequalities #math.DG #msc:53A30 #msc:53A55
paper · pdf · doi:10.48550/arxiv.1301.4742
19 pages. Comments are welcome
openalex publication_date 2013/01/21 · arxiv created 2013/01/22 · arxiv updated 2013/01/23 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
A submanifold in space forms satisfies the well-known DDVV inequality due to De Smet, Dillen, Verstraelen and Vrancken. The submanifold attaining equality in the DDVV inequality at every point is called Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are studied in this paper using the framework of Möbius geometry. We classify Wintgen ideal submanfiolds of dimension m>2 and arbitrary codimension when a canonically defined 2-dimensional distribution \mathbbD is integrable. Such examples come from cones, cylinders, or rotational submanifolds over super-minimal surfaces in spheres, Euclidean spaces, or hyperbolic spaces, respectively.