A $G_2$-Hilbert functional in $G_2$-geometry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915282772033536 |
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| author | Gianniotis, Panagiotis Zacharopoulos, George |
| author_facet | Gianniotis, Panagiotis Zacharopoulos, George |
| contents | In this paper we introduce a new functional on the space of $G_2$-structures which we call the $G_2$-Hilbert functional. It is uniquely determined by a few basic principles inspired by the Einstein-Hilbert functional in Riemannian Geometry, and it has similar variational behaviour with it. For instance, torsion-free and nearly $G_2$-structures are saddle critical points of the volume-normalized $G_2$-Hilbert functional. This allows us to uniquely distinguish two new flows of $G_2$-structures, which can be considered as analogues of the Ricci flow in $G_2$-geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06872 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $G_2$-Hilbert functional in $G_2$-geometry Gianniotis, Panagiotis Zacharopoulos, George Differential Geometry In this paper we introduce a new functional on the space of $G_2$-structures which we call the $G_2$-Hilbert functional. It is uniquely determined by a few basic principles inspired by the Einstein-Hilbert functional in Riemannian Geometry, and it has similar variational behaviour with it. For instance, torsion-free and nearly $G_2$-structures are saddle critical points of the volume-normalized $G_2$-Hilbert functional. This allows us to uniquely distinguish two new flows of $G_2$-structures, which can be considered as analogues of the Ricci flow in $G_2$-geometry. |
| title | A $G_2$-Hilbert functional in $G_2$-geometry |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.06872 |