2013/07/07 by Bang‐Yen Chen, Bang-Yen Chen, Chen, Bang-Yen · 4 citations
Mathematics · #Center of curvature #Combinatorics #Constant-mean-curvature surface #Curvature #Differential Geometry #Differential Geometry (math.DG) #Ellipse #Euclidean geometry #Euclidean space #FOS: Mathematics #Gaussian curvature #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Ideal (ethics) #Mathematical analysis #Mathematics #Mean curvature #Point processes and geometric inequalities #Pure mathematics #Space (punctuation) #Space form #Submanifold #Surface (topology) #Willmore energy #math.DG
paper · pdf · doi:10.48550/arxiv.1307.1825
published in arXiv (Cornell University) (Cornell University) · 18 pages. Published in "Riemannian Geometry and Applications", Proceedings of Conference RIGA 2011, Bucharest, Romania
arxiv created 2013/07/07 · openalex publication_date 2013/07/07 · arxiv updated 2013/07/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Wintgen proved in [P. Wintgen, Sur l'inégalité de Chen-Willmore, C. R. Acad. Sci. Paris, 288 (1979), 993--995] that the Gauss curvature K and the normal curvature KD of a surface in the Euclidean 4-space E4 satisfy K+|KD|≤ H2, where H2 is the squared mean curvature. A surface M in \E4 is called a Wintgen ideal surface if it satisfies the equality case of the inequality identically. Wintgen ideal surfaces in E4 form an important family of surfaces; namely, surfaces with circular ellipse of curvature. In this paper, we provide a brief survey on some old and recent results on Wintgen ideal surfaces and more generally Wintgen ideal submanifolds in definite and indefinite real space forms.