Extrinsically homogeneous Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911801110691840 |
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| author | Anarella, Mateo |
| author_facet | Anarella, Mateo |
| contents | We consider the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ and we study its Lagrangian submanifolds. We provide examples of Lagrangian submanifolds which do not have an analogue in $\mathbb{S}^3\times\mathbb{S}^3$. We also provide an expression for the isometry group of $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ with the pseudo-Riemannian nearly Kähler metric. The main result is a complete classification of extrinsically homogeneous Lagrangian submanifolds in this space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_11962 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extrinsically homogeneous Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ Anarella, Mateo Differential Geometry 53C42 We consider the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ and we study its Lagrangian submanifolds. We provide examples of Lagrangian submanifolds which do not have an analogue in $\mathbb{S}^3\times\mathbb{S}^3$. We also provide an expression for the isometry group of $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ with the pseudo-Riemannian nearly Kähler metric. The main result is a complete classification of extrinsically homogeneous Lagrangian submanifolds in this space. |
| title | Extrinsically homogeneous Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ |
| topic | Differential Geometry 53C42 |
| url | https://arxiv.org/abs/2403.11962 |