Classification of homogeneous holomorphic two-spheres in complex Grassmann manifolds

DOI10.1016/J.DIFGEO.2018.09.005zbMath1410.53061OpenAlexW2895467740WikidataQ115355049 ScholiaQ115355049MaRDI QIDQ1733239

Jie Fei

Publication date: 21 March 2019

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

Full work available at URL: https://doi.org/10.1016/j.difgeo.2018.09.005

zbMATH Keywords

second fundamental formGaussian curvatureVeronese surfaceshomogeneous holomorphic 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)

Related Items (3)

Rigidity of homogeneous holomorphic \(S^2\) in a complex Grassmann manifold \(G(2, N)\) ⋮ 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

• Classification of minimal homogeneous two-spheres in the complex Grassmann manifold \(G(2, n)\)
• Harmonic maps from surfaces to complex projective spaces
• Rigidity of holomorphic curves of constant curvature in \(G(2,5)\)
• The construction of harmonic maps into complex Grassmannians
• 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)
• On Cartan's method of Lie groups and moving frames as applied to uniqueness and existence questions in differential geometry
• Constant curved minimal 2-spheres in \(G(2,4)\)
• Classification of holomorphic spheres of constant curvature in complex Grassmann manifold \(\mathbf G_{2,5}\)
• On the classification of homogeneous 2-spheres in complex Grassmannians
• Isometric imbedding of complex manifolds
• The explicit construction and parametrization of all harmonic maps from the two-sphere to a complex Grassmannian.
• Rigidity of Pseudo-Holomorphic Curves of Constant Curvature in Grassmann Manifolds

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