On the classification of homogeneous 2-spheres in complex Grassmannians

zbMath1263.53052MaRDI QIDQ1948068

Xiaoxiang Jiao, Jie Fei, Liang Xiao, Xiao-Wei Xu

Publication date: 30 April 2013

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1364390422

zbMATH Keywords

unitary representationsspecial unitary groupnon-homogeneous holomorphic 2-sphere

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 (15)

Classfication of homogeneous two-spheres in \(G(2, 5; \mathbb{C})\) ⋮ Minimal two-spheres in \(G(2, 4; (C))\) with parallel second fundamental form ⋮ Construction of conformal minimal two-spheres in quaternionic projective spaces by twistor map ⋮ Classification of homogeneous minimal immersions from \(S^2\) to \({\mathbb {H}}P^n\) ⋮ 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 ⋮ Minimal two-spheres with constant curvature in the quaternionic projective space ⋮ 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 ⋮ Holomorphic isometric embeddings of the projective line into quadrics ⋮ Classification of homogeneous holomorphic two-spheres in complex Grassmann manifolds ⋮ Classification of minimal homogeneous two-spheres in the complex Grassmann manifold \(G(2, n)\) ⋮ Minimal two-spheres with constant curvature in the complex hyperquadric ⋮ 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

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• Minimal immersions of surfaces in Euclidean spheres
• Representations of compact groups and minimal immersions into spheres
• Minimal immersions of spheres into spheres
• Minimal Surfaces by Moving Frames
• Minimal Surfaces of Constant Curvature in S n
• Rigidity of Pseudo-Holomorphic Curves of Constant Curvature in Grassmann Manifolds

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