Cosymplectic Chern--Hamilton conjecture
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912905021095936 |
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| author | Dyhr, Søren González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel |
| author_facet | Dyhr, Søren González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel |
| contents | In this paper, we study the Chern-Hamilton energy functional on compact cosymplectic manifolds, fully classifying in dimension 3 those manifolds admitting a critical compatible metric for this functional. This is the case if and only if either the manifold is co-Kähler or if it is a mapping torus of the 2-torus by a hyperbolic toral automorphism and equipped with a suspension cosymplectic structure. Moreover, any critical metric has minimal energy among all compatible metrics. We also exhibit examples of manifolds with first Betti number $b_1 \geq 2$ admitting cosymplectic structures, but such that no cosymplectic structure admits a critical compatible metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_10379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cosymplectic Chern--Hamilton conjecture Dyhr, Søren González-Prieto, Ángel Miranda, Eva Peralta-Salas, Daniel Differential Geometry Dynamical Systems Symplectic Geometry 53D35 (Primary) 57K35, 37K58, 37D20 (Secondary) In this paper, we study the Chern-Hamilton energy functional on compact cosymplectic manifolds, fully classifying in dimension 3 those manifolds admitting a critical compatible metric for this functional. This is the case if and only if either the manifold is co-Kähler or if it is a mapping torus of the 2-torus by a hyperbolic toral automorphism and equipped with a suspension cosymplectic structure. Moreover, any critical metric has minimal energy among all compatible metrics. We also exhibit examples of manifolds with first Betti number $b_1 \geq 2$ admitting cosymplectic structures, but such that no cosymplectic structure admits a critical compatible metric. |
| title | Cosymplectic Chern--Hamilton conjecture |
| topic | Differential Geometry Dynamical Systems Symplectic Geometry 53D35 (Primary) 57K35, 37K58, 37D20 (Secondary) |
| url | https://arxiv.org/abs/2505.10379 |