Minimal immersions of surfaces into 4-dimensional space forms

zbMath0573.53036MaRDI QIDQ1063266

Irwen Válle Guadalupe, Renato de Azevedo Tribuzy

Publication date: 1985

Published in: Rendiconti del Seminario Matematico della Università di Padova (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/107978

zbMATH Keywords

Clifford torusVeronese surfacenormal curvatureminimal immersion

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (13)

Minimal 2-tori in \(S^ 4\) whose Gauss images have constant curvature ⋮ Exceptional minimal surfaces in spheres ⋮ Constant mean curvature surfaces in 4-space forms ⋮ Branch points of conformal mappings of surfaces ⋮ Boundary value problems for local and nonlocal Liouville type equations with several exponential type nonlinearities: radial and nonradial solutions ⋮ Minimal immersions of surfaces into \(n\)-dimensional space forms ⋮ Timelike surfaces with zero mean curvature in Minkowski 4-space ⋮ Minimal Lorentz surfaces in pseudo-Euclidean 4-space with neutral metric ⋮ The lifts of surfaces in neutral 4-manifolds into the 2-Grassmann bundles ⋮ Minimal hypersurfaces in \(S^ 4\) with vanishing Gauss-Kronecker curvature ⋮ Canonical coordinates and natural equations for minimal time-like surfaces in \(\mathbf{R}^4_2\) ⋮ Lorentzian stationary surfaces and null curves in \({\mathbb R^4_2}\) ⋮ Spacelike maximal surfaces in 4-dimensional space forms of index 2.

Cites Work

• Normal curvature of surfaces in space forms
• Immersions of surfaces into 4-dimensional spaces with nonzero normal curvature
• Minimal immersions of surfaces in Euclidean spheres
• On singularities of submanifolds of higher dimensional Euclidean spaces
• Representations of compact groups and minimal immersions into spheres
• Complete minimal surfaces in \(S^ 3\)
• Some intrinsic characterizations of minimal surfaces
• Minimal surfaces in $4$-dimensional Riemannian manifolds of constant curvature
• Contributions to the Theory of Surfaces in a 4-Space of Constant Curvature
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