Isoparametric foliations and complex structures
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866912230959742976 |
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| author | Qian, Chao Tang, Zizhou Yan, Wenjiao |
| author_facet | Qian, Chao Tang, Zizhou Yan, Wenjiao |
| contents | Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit sphere, as well as on focal submanifolds $M_+$ of OT-FKM type with $g=4$, $m=2$ and $m=4$ in the definite case. Furthermore, we investigate the existence and non-existence of invariant (almost) complex structures on homogeneous isoparametric hypersurfaces with $g=4$, providing a complete classification of those that admit such structures. Finally, we discuss the geometric properties of the complex structures arising from isoparametric theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09041 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Isoparametric foliations and complex structures Qian, Chao Tang, Zizhou Yan, Wenjiao Differential Geometry Complex Variables Explicit representations of complex structures on closed manifolds are valuable, but relatively rare in the literature. Using isoparametric theory, we construct complex structures on isoparametric hypersurfaces with $g=4, m=1$ in the unit sphere, as well as on focal submanifolds $M_+$ of OT-FKM type with $g=4$, $m=2$ and $m=4$ in the definite case. Furthermore, we investigate the existence and non-existence of invariant (almost) complex structures on homogeneous isoparametric hypersurfaces with $g=4$, providing a complete classification of those that admit such structures. Finally, we discuss the geometric properties of the complex structures arising from isoparametric theory. |
| title | Isoparametric foliations and complex structures |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2502.09041 |