Surfaces with parallel mean curvature in \(S^{3}\times \mathbb R\) and \(H^{3}\times \mathbb R\)

DOI10.1307/mmj/1353098510zbMath1268.53006arXiv1103.6254OpenAlexW1521866964MaRDI QIDQ1931923

Dorel Fetcu, Harold Rosenberg

Publication date: 16 January 2013

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.6254

zbMATH Keywords

minimal surfaceRiemannian productparallel mean curvatureSimons formula

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 (11)

Parallel mean curvature tori in \(\mathbb{C}P^2\) and \(\mathbb{C}H^2\) ⋮ Constant mean curvature hypersurfaces with constant angle in semi-Riemannian space forms ⋮ Biharmonic submanifolds with parallel mean curvature in \(\mathbb{S}^{n}\times\mathbb{R}\) ⋮ On the moduli space of isometric surfaces with the same mean curvature in 4-dimensional space forms ⋮ Submanifolds with parallel mean curvature vector field in product spaces ⋮ Gap theorems for submanifolds in \(\mathbb{H}^n\times\mathbb{R}\) ⋮ A classification result for helix surfaces with parallel mean curvature in product spaces ⋮ Fatou-Bieberbach domains in \(\mathbb C^n\setminus\mathbb R^k\) ⋮ Constant mean curvature surfaces in \({\mathbb {M}}^2(c)\times \mathbb {R}\) and finite total curvature ⋮ Complete parallel mean curvature surfaces in two-dimensional complex space-forms ⋮ Four classes of surfaces with constant mean curvature in \(S^3\times\mathbb R\) and \(H^3\times\mathbb R\)

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