On the periodicity of planes with parallel mean curvature vector in \(\mathbb{C} H^2\)

DOI10.3836/tjm/1244208405zbMath1081.53053OpenAlexW1999548922MaRDI QIDQ1768120

Shinya Hirakawa

Publication date: 14 March 2005

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

Full work available at URL: https://doi.org/10.3836/tjm/1244208405

zbMATH Keywords

mean curvatureimmersioncomplex hyperbolicisometric

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (4)

Parallel mean curvature tori in \(\mathbb{C}P^2\) and \(\mathbb{C}H^2\) ⋮ Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes ⋮ Complete parallel mean curvature surfaces in two-dimensional complex space-forms ⋮ Constant Gaussian curvature surfaces with parallel mean curvature vector in two-dimensional complex space forms

Cites Work

• On minimal immersions of \(R^ 2\) into \(P^ n(C)\)
• Minimal surfaces with constant curvature and Kähler angle in complex space forms
• Flat totally real submanifolds of \(CP^ n\) and the symmetric generalized wave equation
• Families of flat minimal tori in \(\mathbb{C} P^ n\)
• Surfaces with parallel mean curvature vector in \(P^ 2(\mathbb C)\)
• Slant immersions
• The classification of the surfaces with parallel mean curvature vector in two-dimensional complex space forms

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