Compact surfaces with constant Gaussian curvature in product spaces

DOI10.1007/S00009-010-0033-4zbMATH Open1201.53064OpenAlexW2092019543MaRDI QIDQ711437

Juan A. Aledo, José A. Pastor, Victorino Lozano

Publication date: 26 October 2010

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-010-0033-4

zbMATH Keywords

Gaussian curvatureproduct spacerotational surfacearea estimatecompact surface with boundary

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20)

Cites Work

• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• Complete surfaces of constant curvature in \(H^{2} \times \mathbb R\) and \(S^{2} \times \mathbb R\)
• Complete surfaces with positive extrinsic curvature in product spaces
• Examples and structure of CMC surfaces in some Riemannian and Lorentzian homogeneous spaces
• Surfaces with constant curvature in \(S^{2}\times \mathbb R\) and \(H^{2}\times \mathbb R\). Height estimates and representation
• Embedded isolated singularities of flat surfaces in hyperbolic 3-space
• On the scalar curvature of hypersurfaces in spaces with a Killing field
• Estimates in surfaces with positive constant Gauss curvature

Related Items (3)

Graph Surfaces Invariant by Parabolic screw Motions with Constant Curvature in $ \: \mathbb H^2 \times \mathbb R$ ⋮ Complete surfaces in the product spaces \(\mathbb{Q}_{\varepsilon}^{2}\times \mathbb{S}^{1}\) with constant Gaussian curvature ⋮ Complete surfaces with positive extrinsic curvature in product spaces

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