Quantization of Curvature of Harmonic Two-Spheres in Grassmann Manifolds

DOI10.2307/2001280zbMath0676.53069OpenAlexW4241080401MaRDI QIDQ3831645

Yunbo Zheng

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001280

zbMATH Keywords

constant curvatureGrassmann manifoldsGaussian curvatureholomorphic mapminimal two-spheresantiholomorphic mapharmonic isometric immersion

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (9)

Counterexamples to the conjecture on minimal \(S^ 2\) in \(\mathbb{C} P^ n\) with constant Kaehler angle ⋮ On conformal minimal 2-spheres in complex Grassmann manifold \(G(2,n)\) ⋮ Holomorphic two-spheres in complex Grassmann manifold \(G(2, 4)\) ⋮ Holomorphic two-spheres in the complex Grassmann manifold \(G(k, n)\) ⋮ On holomorphic curves in a complex Grassmann manifold \(G(2,n)\) ⋮ Minimal two-spheres in \(G(2,4)\) ⋮ Pseudo-holomorphic curves in complex Grassmann manifolds ⋮ Minimal two-spheres with constant curvature in the complex hyperquadric ⋮ Rigidity theorems for holomorphic curves in a complex Grassmann manifold G(3,6)

Cites Work

• Harmonic maps from surfaces to complex projective spaces
• The fundamental equations of minimal surfaces in \({\mathbb{C}}P^ 2\)
• Harmonic maps from \(S^ 2\) to \(G_{2,4}\)
• Harmonic maps of the two-sphere into a complex Grassmann manifold. II
• On conformal minimal immersions of \(S^ 2\) into \({\mathbb{C}}P^ n\)
• A Rigidity Result for Holomorphic Immersions of Surfaces in C P n
• Rigidity of Pseudo-Holomorphic Curves of Constant Curvature in Grassmann Manifolds
• Stable harmonic 2-spheres in symmetric spaces

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