The space of closed $G2$-structures. II. concavity and hypersymplectic structures
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911079448182784 |
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| author | Zheng, Kai |
| author_facet | Zheng, Kai |
| contents | In the space of closed $G_2$-structures equipped with Bryant's Dirichlet-type metric, we continue to utilise the geodesic, constructed in our previous article, to show that, under a normalisation condition Hitchin's volume functional is geodesically concave and the $G_2$ Laplacian flow decreases the length. Furthermore, we also construct various examples of hyper-symplectic manifolds on geodesic concavity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20456 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The space of closed $G2$-structures. II. concavity and hypersymplectic structures Zheng, Kai Differential Geometry Symplectic Geometry In the space of closed $G_2$-structures equipped with Bryant's Dirichlet-type metric, we continue to utilise the geodesic, constructed in our previous article, to show that, under a normalisation condition Hitchin's volume functional is geodesically concave and the $G_2$ Laplacian flow decreases the length. Furthermore, we also construct various examples of hyper-symplectic manifolds on geodesic concavity. |
| title | The space of closed $G2$-structures. II. concavity and hypersymplectic structures |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2507.20456 |