Hyperkähler structures on leaves of hyper-Lie Poisson manifolds
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914425675448320 |
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| author | Ni, Dadi Qi, Kaichuan |
| author_facet | Ni, Dadi Qi, Kaichuan |
| contents | Due to its rich structure and close connection with gauge theory, hyperkähler manifolds have attracted increasing interest. Using infinite dimensional hyperkähler reduction, Kronheimer proved that certain adjoint orbits of complexified semisimple Lie algebras admits hyperkähler structures. Later on, Xu obtained a proof for the existence of hyperkähler structures on adjoint orbits of $\mathfrak{sl}(2,\mathbb{C})$ from the viewpoint of symplectic geometry. This paper aims to thoroughly investigate and elucidate the key differences as well as the underlying connections between two distinct construction methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hyperkähler structures on leaves of hyper-Lie Poisson manifolds Ni, Dadi Qi, Kaichuan Differential Geometry Symplectic Geometry Due to its rich structure and close connection with gauge theory, hyperkähler manifolds have attracted increasing interest. Using infinite dimensional hyperkähler reduction, Kronheimer proved that certain adjoint orbits of complexified semisimple Lie algebras admits hyperkähler structures. Later on, Xu obtained a proof for the existence of hyperkähler structures on adjoint orbits of $\mathfrak{sl}(2,\mathbb{C})$ from the viewpoint of symplectic geometry. This paper aims to thoroughly investigate and elucidate the key differences as well as the underlying connections between two distinct construction methods. |
| title | Hyperkähler structures on leaves of hyper-Lie Poisson manifolds |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2502.08979 |