Minimal surfaces in \(\mathbb{S}^{2} \times \mathbb{S}^{2}\)

DOI10.1007/s12220-013-9460-3zbMath1326.53084arXiv1301.1580OpenAlexW1979384109MaRDI QIDQ2347943

Francisco Torralbo, Francisco Urbano

Publication date: 10 June 2015

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.1580

zbMATH Keywords

totally geodesicLaplacianHopf differentialFrenet equationsWeierstrass torus

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40) Differentials on Riemann surfaces (30F30)

Related Items (12)

Minimal surfaces in the product of two dimensional real space forms endowed with a neutral metric ⋮ The Gauss map of minimal surfaces in \({\mathbb{S}}^2 \times{\mathbb{R}} \) ⋮ Constant mean curvature isometric immersions into \(\mathbb{S}^2\times\mathbb{R}\) and \(\mathbb{H}^2\times\mathbb{R}\) and related results ⋮ Minimal Lagrangian submanifolds of the complex hyperquadric ⋮ Gauss maps of harmonic and minimal great circle fibrations ⋮ On Hopf hypersurfaces of \(\mathbb{S}^2 \times \mathbb{S}^2\) and \(\mathbb{H}^2 \times \mathbb{H}^2\) ⋮ A fundamental theorem for submanifolds of multiproducts of real space forms ⋮ A geometrical correspondence between maximal surfaces in anti-de Sitter space-time and minimal surfaces in \(\mathbb H^2\times\mathbb R\) ⋮ On stability and index of minimal submanifolds ⋮ A Schwarz-Pick lemma for minimal maps ⋮ On the geometry of hypersurfaces in \({\mathbb{S}}^2 \times{\mathbb{S}}^2 \) ⋮ On real hypersurfaces of 𝕊²×𝕊²

Cites Work

• Unnamed Item
• Finite type minimal annuli in \(\mathbb{S}^{2}\times\mathbb{R}\)
• The fundamental equations of minimal surfaces in \({\mathbb{C}}P^ 2\)
• Minimal surfaces in Kähler surfaces and Ricci curvature
• Conformal and minimal immersions of compact surfaces into the 4-sphere
• A new conformal invariant and its applications to the Willmore conjecture and the first eigenvalue of compact surfaces
• Eigenfunctions and nodal sets
• Totally geodesic submanifolds of symmetric spaces. I
• On univalent harmonic maps between surfaces
• The second variation of area of minimal surfaces in four-manifolds
• Harmonic maps from a 2-torus to the 3-sphere
• Minimal Lagrangian surfaces in \(\mathbb S^2 \times \mathbb S^2\)
• Complete minimal surfaces in \(S^ 3\)
• Surfaces with parallel mean curvature vector in $\mathbb{S}^{2}×\mathbb{S}^{2}$ and $\mathbb{H}^{2}×\mathbb{H}^{2}$
• Second variation of superminimal surfaces into self-dual Einstein four-manifolds
• On stable compact minimal submanifolds
• The Tension Field of the Gauss Map

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