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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2601.18504 |
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| _version_ | 1866910001185947648 |
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| author | Liefsoens, Michaël Van der Veken, Joeri |
| author_facet | Liefsoens, Michaël Van der Veken, Joeri |
| contents | A tractable definition of the homogeneous nearly Kähler structure on $\mathbb{C}P^3$ is given via the Hopf fibration, facilitating explicit computations and analysis. The description extends to all homogeneous metrics on $\mathbb{C}P^3$, providing expressions for their Riemann curvature tensors and full isometry groups. Rigid immersions are presented for all extrinsically homogeneous Lagrangian submanifolds in the nearly Kähler $\mathbb{C}P^3$, and the nonexistence of Lagrangians with constant sectional curvature is established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18504 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Curvature and Lagrangian submanifolds of the homogeneous nearly Kähler $\mathbb{C}P^3$ Liefsoens, Michaël Van der Veken, Joeri Differential Geometry A tractable definition of the homogeneous nearly Kähler structure on $\mathbb{C}P^3$ is given via the Hopf fibration, facilitating explicit computations and analysis. The description extends to all homogeneous metrics on $\mathbb{C}P^3$, providing expressions for their Riemann curvature tensors and full isometry groups. Rigid immersions are presented for all extrinsically homogeneous Lagrangian submanifolds in the nearly Kähler $\mathbb{C}P^3$, and the nonexistence of Lagrangians with constant sectional curvature is established. |
| title | Curvature and Lagrangian submanifolds of the homogeneous nearly Kähler $\mathbb{C}P^3$ |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2601.18504 |