Abstract
In this paper, we give a local rigid characterization of all homogeneous holomorphic two-spheres in a complex Grassmann manifold G(2, N). Let κ denote the new global invariant defined in terms of the square norm of (1, 0) part of the second-order covariant differential of the first ∂ -transform for a holomorphic curve in G(2, N). It is proved that a linearly full non-degenerate holomorphic curve of constant curvature and constant square norm of the second fundamental form in G(2, N) with κ= 0 must be homogeneous.
Original language | English |
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Article number | 324 |
Journal | Journal of Geometric Analysis |
Volume | 33 |
Issue number | 10 |
DOIs | |
Publication status | Published - Oct 2023 |
Keywords
- Complex Grassmann manifolds
- Gaussian curvature
- Holomorphic curves
- Rigidity
- The second fundamental form
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Fei, J., He, L., & Wang, J. (2023). Rigidity of Homogeneous Holomorphic S2 in a Complex Grassmann Manifold G(2, N). Journal of Geometric Analysis, 33(10), Article 324. https://doi.org/10.1007/s12220-023-01387-7