Classification of Wintgen ideal surfaces in Euclidean 4-space with equal Gauss and normal curvatures

DOI10.1007/s10455-010-9205-5zbMath1203.53005OpenAlexW2071501314MaRDI QIDQ1959094

Bang-Yen Chen

Publication date: 6 October 2010

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10455-010-9205-5

zbMATH Keywords

Whitney sphereGauss curvaturenormal curvaturesuperminimal surfacesquared mean curvatureWintgen ideal surface

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Surfaces in Euclidean and related spaces (53A05)

Related Items (18)

Pseudo-symmetries of generalized Wintgen ideal Lagrangian submanifolds ⋮ Wintgen ideal submanifolds: new examples, frame sequence and Möbius homogeneous classification ⋮ Pseudosymmetry properties of generalised Wintgen ideal Legendrian submanifolds ⋮ On the normal scalar curvature conjecture for legendrian submanifolds in Kenmotsu space forms ⋮ Generalized Wintgen inequality for submanifolds in generalized (κ, µ)-space forms ⋮ A generalized Wintgen inequality for quaternionic CR-submanifolds ⋮ Wintgen ideal surfaces in four-dimensional neutral indefinite space form \({R^4_2(c)}\) ⋮ On the normal scalar curvature conjecture in Kenmotsu statistical manifolds ⋮ Wintgen ideal submanifolds with vanishing Möbius form ⋮ Invariants and Bonnet-type theorem for surfaces in \(\mathbb R^{4}\) ⋮ Three special classes of Wintgen ideal submanifolds ⋮ Wintgen ideal submanifolds: reduction theorems and a coarse classification ⋮ Wintgen ideal submanifolds with a low-dimensional integrable distribution ⋮ Minimal surfaces in a unit sphere pinched by intrinsic curvature and normal curvature ⋮ Generalized Wintgen inequality for slant submanifolds in metallic Riemannian space forms ⋮ Wintgen inequality for statistical surfaces ⋮ Recent developments in Wintgen inequality and Wintgen ideal submanifolds ⋮ A factorization of a super-conformal map

Cites Work

• Submanifolds with totally geodesic Gauss image
• All superconformal surfaces in \({\mathbb R^4}\) in terms of minimal surfaces
• Normal curvature of surfaces in space forms
• On surfaces in four-spaces
• Conformal and minimal immersions of compact surfaces into the 4-sphere
• Complex extensors and Lagrangian submanifolds in complex Euclidean spaces
• Elliptic functions and applications
• The geometry of the generalized Gauss map
• Lagrangian surfaces with circular ellipse of curvature in complex space forms
• Exact solutions of a class of differential equations of Lamé's type and its applications to contact geometry
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