Classification of conformal minimal immersions of constant curvature from \(S^2\) to \(Q_3\)

DOI10.2969/jmsj/06820863zbMath1357.53069OpenAlexW2338349521MaRDI QIDQ296564

Mingyan Li, Xiaoxiang Jiao, Ling He

Publication date: 23 June 2016

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

Full work available at URL: https://projecteuclid.org/euclid.jmsj/1460727385

zbMATH Keywords

classificationKähler angleGauss curvatureconformal minimal immersioncomplex hyperquadric

Mathematics Subject Classification ID

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

Related Items (11)

Classification of conformal minimal immersions of constant curvature from \(S^2\) to \(Q_n\) ⋮ Classfication of homogeneous two-spheres in \(G(2, 5; \mathbb{C})\) ⋮ Rigidity of conformal minimal immersions of constant curvature from \(S^2\) to \(Q_4\) ⋮ 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 ⋮ Diagrams and harmonic maps, revisited ⋮ Rigidity theorem for holomorphic curves in a hyperquadric \(Q_n\) ⋮ Conformal minimal immersions with constant curvature from \(S^2\) to \(Q_{5}\)

Cites Work

• Totally real minimal surfaces in the complex hyperquadrics
• Pseudo-holomorphic curves of constant curvature in complex Grassmannians
• The construction of harmonic maps into complex Grassmannians
• Harmonic maps of the two-sphere into the complex hyperquadric
• Harmonic maps of the two-sphere into a complex Grassmann manifold. II
• On conformal minimal immersions of \(S^ 2\) into \({\mathbb{C}}P^ n\)
• Minimal surfaces in a complex hyperquadric \(Q _{2}\)
• Classification of conformal minimal immersions of constant curvature from \(S^2\) to \(HP^2\)
• Minimal Surfaces of Constant Curvature in S n
• Harmonic Maps from S ² to G ₂ (C⁵ )
• The explicit construction of all harmonic two-spheres in G2 (Rn).
• Rigidity of Pseudo-Holomorphic Curves of Constant Curvature in Grassmann Manifolds
• The geometry of the generalized Gauss map
• On minimal surfaces of constant curvature in two-dimensional complex space form

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