Submanifolds of codimension two attaining equality in an extrinsic inequality

2008/02/06 by Marcos Dajczer Ruy Tojeiro, Tojeiro, Marcos Dajczer Ruy · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Point processes and geometric inequalities #math.DG

paper · pdf · doi:10.48550/arxiv.0802.0805

arxiv created 2008/02/06 · openalex publication_date 2008/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a parametric construction in terms of minimal surfaces of the Euclidean submanifolds of codimension two and arbitrary dimension that attain equality in an inequality due to De Smet, Dillen, Verstraelen and Vrancken. The latter involves the scalar curvature, the norm of the normal curvature tensor and the length of the mean curvature vector.

Cited by

• Natural Intrinsic Geometrical Symmetries
• Local Wintgen ideal submanifolds
• Möbius geometry of three-dimensional Wintgen ideal submanifolds in \mathbbS⁵

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• A basic inequality for submanifolds in a cosymplectic space form