Totally geodesic 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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| Format: | Preprint |
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2023
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| _version_ | 1866910344554741760 |
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| author | Anarella, Mateo Van der Veken, Joeri |
| author_facet | Anarella, Mateo Van der Veken, Joeri |
| contents | In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$. First, we show that they split into four different classes depending on their behaviour with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13389 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Totally geodesic Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$ Anarella, Mateo Van der Veken, Joeri Differential Geometry 53C42 In this paper, we study Lagrangian submanifolds of the pseudo-nearly Kähler $\mathrm{SL}(2,\mathbb{R})\times\mathrm{SL}(2,\mathbb{R})$. First, we show that they split into four different classes depending on their behaviour with respect to a certain almost product structure on the ambient space. Then, we give a complete classification of totally geodesic Lagrangian submanifolds of this space. |
| title | Totally geodesic 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/2307.13389 |