On characteristic foliations of metric contact-symplectic structures
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910010104086528 |
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| author | Hadjar, Amine |
| author_facet | Hadjar, Amine |
| contents | We study compatible and associated metrics for a contact-symplectic pair $(η, ω)$ on a manifold. We show that the integral curves of the Reeb vector field are geodesics for any compatible metric. We prove that all associated metrics share a common volume element, which we give explicitly. When the characteristic foliations of $η$ and $ω$ are orthogonal with respect to an associated metric, their leaves, as well as those of the characteristic foliation of $dη$, are minimal. We construct explicit examples on nilpotent Lie groups and nilmanifolds where the characteristic foliations are not both totally geodesic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_03356 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On characteristic foliations of metric contact-symplectic structures Hadjar, Amine Differential Geometry Primary 53C25, secondary 53B20, 53D10, 53B35, 53C12 We study compatible and associated metrics for a contact-symplectic pair $(η, ω)$ on a manifold. We show that the integral curves of the Reeb vector field are geodesics for any compatible metric. We prove that all associated metrics share a common volume element, which we give explicitly. When the characteristic foliations of $η$ and $ω$ are orthogonal with respect to an associated metric, their leaves, as well as those of the characteristic foliation of $dη$, are minimal. We construct explicit examples on nilpotent Lie groups and nilmanifolds where the characteristic foliations are not both totally geodesic. |
| title | On characteristic foliations of metric contact-symplectic structures |
| topic | Differential Geometry Primary 53C25, secondary 53B20, 53D10, 53B35, 53C12 |
| url | https://arxiv.org/abs/2602.03356 |