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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.02074 |
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| _version_ | 1866914527501615104 |
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| author | Saavedra, Julieth |
| author_facet | Saavedra, Julieth |
| contents | In this paper, we study critical points and gradient flows of the $G_2$--Hilbert functional on a manifolds with free $\mathbb S^1$--actions. We analyze $\mathbb S^1$--invariant $G_2$--structures under the constant fiber-length non-Kähler transverse ansatz, reducing the variational problem to the $6$--dimensional quotient and we also consider a Gibbons--Hawking-type ansatz with varying fiber length and derive the formal negative $L^2$--gradient flow. We conclude that the unnormalized flow admits only trivial stationary configurations: flat connection, scalar-flat base metric, and constant fiber length. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02074 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Geometric Reductions of the $G_2$-Hilbert Functional via Circle Actions Saavedra, Julieth Differential Geometry In this paper, we study critical points and gradient flows of the $G_2$--Hilbert functional on a manifolds with free $\mathbb S^1$--actions. We analyze $\mathbb S^1$--invariant $G_2$--structures under the constant fiber-length non-Kähler transverse ansatz, reducing the variational problem to the $6$--dimensional quotient and we also consider a Gibbons--Hawking-type ansatz with varying fiber length and derive the formal negative $L^2$--gradient flow. We conclude that the unnormalized flow admits only trivial stationary configurations: flat connection, scalar-flat base metric, and constant fiber length. |
| title | Geometric Reductions of the $G_2$-Hilbert Functional via Circle Actions |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2605.02074 |