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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2509.21809 |
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| _version_ | 1866912607792791552 |
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| author | Nakova, Galia Bejan, Cornelia-Livia |
| author_facet | Nakova, Galia Bejan, Cornelia-Livia |
| contents | In this paper we construct and study almost paracontact metric structures $(φ,ξ,η,g)$ on a 3-dimensional Walker manifold $(M,g)$ with respect to a local basis only by the coordinate functions of a unit space-like vector field $ξ$, globally defined on $M$ and a function $f$ on $M$, characterizing the Lorentzian metric $g$. Necessary and sufficient conditions are obtained for $M$, endowed with these structures, to fall in one of the following classes of 3-dimensional almost paracontact metric manifolds according to the classification given by S. Zamkovoy and G. Nakova: paracontact metric, normal, almost $α$-paracosymplectic, almost paracosymplectic, paracosymplectic and $\mathbb{G}_{12}$-manifolds. Also, classes to which the studied manifolds do not belong are found. Special attention is paid to an $η$-Einstein manifold among the considered manifolds and its $ξ$-sectional, $φ$-sectional and scalar curvature are investigated. Examples of the examined manifolds are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Almost paracontact metric 3-dimensional Walker manifolds Nakova, Galia Bejan, Cornelia-Livia Differential Geometry 53C15, 53C50 In this paper we construct and study almost paracontact metric structures $(φ,ξ,η,g)$ on a 3-dimensional Walker manifold $(M,g)$ with respect to a local basis only by the coordinate functions of a unit space-like vector field $ξ$, globally defined on $M$ and a function $f$ on $M$, characterizing the Lorentzian metric $g$. Necessary and sufficient conditions are obtained for $M$, endowed with these structures, to fall in one of the following classes of 3-dimensional almost paracontact metric manifolds according to the classification given by S. Zamkovoy and G. Nakova: paracontact metric, normal, almost $α$-paracosymplectic, almost paracosymplectic, paracosymplectic and $\mathbb{G}_{12}$-manifolds. Also, classes to which the studied manifolds do not belong are found. Special attention is paid to an $η$-Einstein manifold among the considered manifolds and its $ξ$-sectional, $φ$-sectional and scalar curvature are investigated. Examples of the examined manifolds are given. |
| title | Almost paracontact metric 3-dimensional Walker manifolds |
| topic | Differential Geometry 53C15, 53C50 |
| url | https://arxiv.org/abs/2509.21809 |