Minimal Lagrangian submanifolds with constant sectional curvature in indefinite complex space forms

DOI10.1090/S0002-9939-01-06213-XzbMath0999.53052OpenAlexW2118869889MaRDI QIDQ2781306

Luc Vrancken

Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-01-06213-x

zbMATH Keywords

Lagrangianconstant sectional curvatureindefinite complex space form

Mathematics Subject Classification ID

Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Lagrangian submanifolds; Maslov index (53D12) Local submanifolds (53B25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (7)

Classification of marginally trapped Lagrangian surfaces in Lorentzian complex space forms ⋮ Biharmonic and quasi-biharmonic slant surfaces in Lorentzian complex space forms ⋮ Minimal Lagrangian isotropic immersions in indefinite complex space forms ⋮ Classification of Lagrangian surfaces of constant curvature in complex projective plane ⋮ Classification of Lagrangian surfaces of curvature \(\varepsilon \) in non-flat Lorentzian complex space form \({\tilde M}_1^2 (4\varepsilon)\) ⋮ Classification of Lagrangian surfaces of constant curvature in complex hyperbolic plane ⋮ Pseudo-parallel lorentzian surfaces in pseudo-Riemannian space forms

Cites Work

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• Lagrangian minimal isometric immersions of a Lorentzian real space form into a Lorentzian complex space form
• The Magid-Ryan conjecture for equiaffine hyperspheres with constant sectional curvature.
• An extension of Calabi's rigidity theorem to complex submanifolds of indefinite complex space forms
• Indefinite rigidity of complex submanifolds and maximal surfaces
• Some Examples of Indefinite Complete Complex Einstein Hypersurfaces Not Locally Symmetric
• Totally Real Minimal Immersions of n-Dimensional Real Space Forms into n-Dimensional Complex Space Forms

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