Rigidity of holomorphic curves of constant curvature in \(G(2,5)\)

DOI10.1016/j.difgeo.2015.08.004zbMath1329.53105OpenAlexW2188859703WikidataQ115355861 ScholiaQ115355861MaRDI QIDQ891582

Ling He, Xianchao Zhou, Xiaoxiang Jiao

Publication date: 17 November 2015

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.difgeo.2015.08.004

zbMATH Keywords

classificationholomorphic curveGauss curvatureVeronese curvecomplex Grassmann manifold

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

On non-\(\pm\)holomorphic conformal minimal two-spheres in a complex Grassmannian \(G(2,5)\) with constant curvature ⋮ Classfication of homogeneous two-spheres in \(G(2, 5; \mathbb{C})\) ⋮ Local rigidity of holomorphic curves in the complex Grassmann manifold \(G(2,6)\) ⋮ Homogeneity-preserving property of harmonic sequences from surfaces into complex Grassmann manifolds ⋮ A characterization of homogeneous totally real minimal two-spheres in a complex hyperquadric ⋮ Rigidity of homogeneous holomorphic \(S^2\) in a complex Grassmann manifold \(G(2, N)\) ⋮ A rigidity of equivariant holomorphic maps into a complex Grassmannian induced from orthogonal direct sums of holomorphic line bundles ⋮ Classification of homogeneous holomorphic two-spheres in complex Grassmann manifolds ⋮ Pinching for holomorphic curves in a complex Grassmann manifold \(G(2,n;\mathbb{C})\) ⋮ Rigidity theorems for holomorphic curves in a complex Grassmann manifold G(3,6)

Cites Work

• On conformal minimal 2-spheres in complex Grassmann manifold \(G(2,n)\)
• Constant curvature solutions of Grassmannian sigma models. II: Non-holomorphic solutions
• On holomorphic curves in a complex Grassmann manifold \(G(2,n)\)
• Harmonic maps from surfaces to complex projective spaces
• Pseudo-holomorphic curves of constant curvature in complex Grassmannians
• On pseudo-holomorphic curves from two-spheres into a complex Grassmannian \(G(2,5)\)
• Minimal two-spheres in \(G(2,4)\)
• The construction of harmonic maps into complex Grassmannians
• 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)
• Classification of holomorphic spheres of constant curvature in complex Grassmann manifold \(\mathbf G_{2,5}\)
• Constant curvature solutions of Grassmannian sigma models. I: Holomorphic solutions
• 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