Compatibility of Goldman's symplectic form with the complex structure on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866915340975341568 |
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| author | Emam, Christian El Sagman, Nathaniel |
| author_facet | Emam, Christian El Sagman, Nathaniel |
| contents | We prove that, on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component, the Goldman symplectic form and the Labourie-Loftin complex structure are compatible and together determine a (mapping class group invariant) pseudo-Kähler structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Compatibility of Goldman's symplectic form with the complex structure on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component Emam, Christian El Sagman, Nathaniel Differential Geometry Geometric Topology 20H10 30F60 58E20 We prove that, on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component, the Goldman symplectic form and the Labourie-Loftin complex structure are compatible and together determine a (mapping class group invariant) pseudo-Kähler structure. |
| title | Compatibility of Goldman's symplectic form with the complex structure on the $\mathrm{SL}(3,\mathbb R)$ Hitchin component |
| topic | Differential Geometry Geometric Topology 20H10 30F60 58E20 |
| url | https://arxiv.org/abs/2411.02350 |