Locally conformal almost generalized $f$-cosymplectic manifolds
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866911395563438080 |
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| author | Massamba, Fortuné Mitoueni, Jude Rosnick Bayeni |
| author_facet | Massamba, Fortuné Mitoueni, Jude Rosnick Bayeni |
| contents | This paper introduces a new class of geometric structures in almost contact metric geometry, which we call locally conformal almost generalized $f$-cosymplectic manifolds. These are almost contact metric structures $(ϕ, ξ, η, g)$ equipped with a closed Lee form $ω$ and a smooth function $f$ satisfying $$ dη= ω\wedge η, \;\; dΦ= 2fη\wedge Φ+ 2ω\wedge Φ, $$ where $Φ(\cdot, \cdot) = g(\cdot, ϕ\cdot)$ is the second fundamental form. We derive integrability conditions and prove a dimensional dichotomy: in dimension $3$, $ω$ may admit transverse components, while in higher dimensions it must be proportional to $η$. This rigidity, which contrasts with even-dimensional conformal symplectic geometry, is established and illustrated by explicit examples in dimensions $3$ and $5$. The framework generalizes and unifies prior results on locally conformal almost cosymplectic and almost $f$-cosymplectic structures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Locally conformal almost generalized $f$-cosymplectic manifolds Massamba, Fortuné Mitoueni, Jude Rosnick Bayeni Differential Geometry 53C15, 53C25 This paper introduces a new class of geometric structures in almost contact metric geometry, which we call locally conformal almost generalized $f$-cosymplectic manifolds. These are almost contact metric structures $(ϕ, ξ, η, g)$ equipped with a closed Lee form $ω$ and a smooth function $f$ satisfying $$ dη= ω\wedge η, \;\; dΦ= 2fη\wedge Φ+ 2ω\wedge Φ, $$ where $Φ(\cdot, \cdot) = g(\cdot, ϕ\cdot)$ is the second fundamental form. We derive integrability conditions and prove a dimensional dichotomy: in dimension $3$, $ω$ may admit transverse components, while in higher dimensions it must be proportional to $η$. This rigidity, which contrasts with even-dimensional conformal symplectic geometry, is established and illustrated by explicit examples in dimensions $3$ and $5$. The framework generalizes and unifies prior results on locally conformal almost cosymplectic and almost $f$-cosymplectic structures. |
| title | Locally conformal almost generalized $f$-cosymplectic manifolds |
| topic | Differential Geometry 53C15, 53C25 |
| url | https://arxiv.org/abs/2601.17051 |