On complete submanifolds with parallel mean curvature in product spaces

DOI10.4171/RMI/757zbMath1294.53055arXiv1112.3452WikidataQ125675766 ScholiaQ125675766MaRDI QIDQ2436059

Dorel Fetcu, Harold Rosenberg

Publication date: 21 February 2014

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.3452

zbMATH Keywords

second fundamental formvertical cylinderLaplacian

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 (6)

On complete submanifolds with parallel normalized mean curvature in product spaces ⋮ Submanifolds with parallel mean curvature vector field in product spaces ⋮ Gap theorems for submanifolds in \(\mathbb{H}^n\times\mathbb{R}\) ⋮ Pinching problems of minimal submanifolds in a product space ⋮ A Simons type integral inequality for closed submanifolds in the product space \(\mathbb{S}^n\times\mathbb{R}\) ⋮ The Abresch–Rosenberg shape operator and applications

Cites Work

• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• A Hopf theorem for ambient spaces of dimensions higher than three
• On submanifolds with parallel mean curvature vector
• On the scalar curvature of constant mean curvature hypersurfaces in space forms
• Hypersurfaces with Constant Mean Curvature in Spheres

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