Minimal two-spheres with constant curvature in the complex hyperquadric

DOI10.1016/J.MATPUR.2016.02.017zbMath1343.53059OpenAlexW2288967140MaRDI QIDQ726573

Jun Wang, Chia-kuei Peng, Xiao-Wei Xu

Publication date: 12 July 2016

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matpur.2016.02.017

zbMATH Keywords

Kähler angleconstant curvaturetotally geodesicminimal two-spheres

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20)

Related Items (13)

A characterization of homogeneous holomorphic two-spheres in \(Q_n\) ⋮ Simons-type inequalities for minimal surfaces with constant Kähler angle in a complex hyperquadric ⋮ On conformal minimal immersions with constant curvature from two-spheres into the complex hyperquadrics ⋮ Totally real flat minimal surfaces in the hyperquadric ⋮ Rigidity of holomorphic curves in a hyperquadric \(Q_4\) ⋮ A characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric ⋮ Minimal two-spheres with constant curvature in the quaternionic projective space ⋮ Diagrams and harmonic maps, revisited ⋮ Structure of minimal 2-spheres of constant curvature in the complex hyperquadric ⋮ Superminimal surfaces in hyperquadric \(Q_2\) ⋮ Rigidity theorem for holomorphic curves in a hyperquadric \(Q_n\) ⋮ Conformal minimal immersions with constant curvature from \(S^2\) to \(Q_{5}\) ⋮ Pinching for holomorphic curves in a complex Grassmann manifold \(G(2,n;\mathbb{C})\)

Cites Work

• Unnamed Item
• Unnamed Item
• Totally real minimal surfaces in the complex hyperquadrics
• Constant curvature solutions of Grassmannian sigma models. II: Non-holomorphic solutions
• The dimension and structure of the space of harmonic 2-spheres in the \(m\)-sphere
• Minimal two-spheres with constant curvature in the complex Grassmannians
• Conformal minimal two-spheres in \(Q_{n}\)
• Harmonic maps from surfaces to complex projective spaces
• Harmonic maps of the two-sphere into the complex hyperquadric
• Minimal 2-spheres with constant curvature in \(P_ n({\mathbb C})\)
• Harmonic maps of the two-sphere into a complex Grassmann manifold. II
• On conformal minimal immersions of \(S^ 2\) into \({\mathbb{C}}P^ n\)
• Harmonic maps into Lie groups (classical solutions of the chiral model)
• Constant curved minimal 2-spheres in \(G(2,4)\)
• Classification of holomorphic spheres of constant curvature in complex Grassmann manifold \(\mathbf G_{2,5}\)
• Minimal surfaces in a complex hyperquadric \(Q _{2}\)
• Constant curvature solutions of Grassmannian sigma models. I: Holomorphic solutions
• On the classification of homogeneous 2-spheres in complex Grassmannians
• Classification of homogeneous submanifolds in homogeneous spaces
• Totally real conformal minimal tori in the hyperquadric \(Q_2\)
• Minimal immersions of surfaces in Euclidean spheres
• Minimal immersions of spheres into spheres
• Minimal Surfaces by Moving Frames
• The explicit construction and parametrization of all harmonic maps from the two-sphere to a complex Grassmannian.
• The explicit construction of all harmonic two-spheres in G2 (Rn).
• Rigidity of Pseudo-Holomorphic Curves of Constant Curvature in Grassmann Manifolds
• Quantization of Curvature of Harmonic Two-Spheres in Grassmann Manifolds
• On Minimal Immersions of S 2 Into S 2m
• Pseudo-holomorphic curves in complex Grassmann manifolds

This page was built for publication: Minimal two-spheres with constant curvature in the complex hyperquadric