Constant Gaussian curvature surfaces with parallel mean curvature vector in two-dimensional complex space forms

DOI10.1007/s10711-005-9038-8zbMath1101.53036OpenAlexW1977594308MaRDI QIDQ2498421

Shinya Hirakawa

Publication date: 16 August 2006

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10711-005-9038-8

zbMATH Keywords

complex space formparallel mean curvature vectorconstant Gaussian curvature

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (12)

Parallel mean curvature tori in \(\mathbb{C}P^2\) and \(\mathbb{C}H^2\) ⋮ Special slant surfaces with non-constant mean curvature in 2-dimensional complex space forms ⋮ Constant mean curvature isometric immersions into \(\mathbb{S}^2\times\mathbb{R}\) and \(\mathbb{H}^2\times\mathbb{R}\) and related results ⋮ Symplectic critical surfaces with parallel normalized mean curvature vector in two-dimensional complex space forms ⋮ Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes ⋮ Special Liouville metric with the Ricci condition ⋮ Complete parallel mean curvature surfaces in two-dimensional complex space-forms ⋮ Bernstein-Heinz-Chern results in calibrated manifolds ⋮ Surfaces in self-dual Einstein manifolds and their twistor lifts ⋮ Surfaces in four-dimensional hyperkähler manifolds whose twistor lifts are harmonic sections ⋮ Minimal surfaces in the complex hyperquadric $Q_2$ II ⋮ Surfaces with parallel mean curvature in ℂℙⁿ×ℝ and ℂℍⁿ×ℝ

Cites Work

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• The fundamental equations of minimal surfaces in \({\mathbb{C}}P^ 2\)
• Special slant surfaces and a basic inequality
• On the periodicity of planes with parallel mean curvature vector in \(\mathbb{C} H^2\)
• Surfaces of constant mean curvature in manifolds of constant curvature
• On the overdetermined system about surfaces with parallel mean curvature vector field.
• Flat totally real submanifolds of \(CP^ n\) and the symmetric generalized wave equation
• Surfaces with parallel mean curvature vector in \(P^ 2(\mathbb C)\)
• Submanifolds with Constant Mean Curvature
• The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms

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