Conformal vector fields on almost Kenmotsu manifolds
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916112816406528 |
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| author | De, Uday Chand Sardar, Arpan De, Krishnendu |
| author_facet | De, Uday Chand Sardar, Arpan De, Krishnendu |
| contents | In this paper, first we consider that the conformal vector field $\mathbf{X}$ is identical with the Reeb vector field $ς$ and next, assume that $\mathbf{X}$ is pointwise collinear with %the Reeb vector field $ς$, in both cases it is shown that the manifold $\mathbf{N}^{2m+1}$ becomes a Kenmotsu manifold and $\mathbf{N}^{2m+1}$ is locally a warped product $\mathbf{N}' \times_{f} \mathbf{M}^{2m}$, where $\mathbf{M}^{2m}$ is an almost Kähler manifold, $\mathbf{N}'$ is an open interval with coordinate t, and $f = ce^{t}$ for some positive constant c. Beside these, we prove that if a $(\verb"k",\boldsymbolμ)'$-almost Kenmotsu manifold admits a Killing vector field $\mathbf{X}$, then either it is locally a warped product of an almost Kähler manifold and an open interval or $\mathbf{X}$ is a strict infinitesimal contact transformation. Furthermore, we also investigate $\boldsymbolη$-Ricci-Yamabe soliton with conformal vector fields on $(\verb"k",\boldsymbolμ)'$-almost Kenmotsu manifolds and finally, we construct an example. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_01425 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal vector fields on almost Kenmotsu manifolds De, Uday Chand Sardar, Arpan De, Krishnendu Differential Geometry In this paper, first we consider that the conformal vector field $\mathbf{X}$ is identical with the Reeb vector field $ς$ and next, assume that $\mathbf{X}$ is pointwise collinear with %the Reeb vector field $ς$, in both cases it is shown that the manifold $\mathbf{N}^{2m+1}$ becomes a Kenmotsu manifold and $\mathbf{N}^{2m+1}$ is locally a warped product $\mathbf{N}' \times_{f} \mathbf{M}^{2m}$, where $\mathbf{M}^{2m}$ is an almost Kähler manifold, $\mathbf{N}'$ is an open interval with coordinate t, and $f = ce^{t}$ for some positive constant c. Beside these, we prove that if a $(\verb"k",\boldsymbolμ)'$-almost Kenmotsu manifold admits a Killing vector field $\mathbf{X}$, then either it is locally a warped product of an almost Kähler manifold and an open interval or $\mathbf{X}$ is a strict infinitesimal contact transformation. Furthermore, we also investigate $\boldsymbolη$-Ricci-Yamabe soliton with conformal vector fields on $(\verb"k",\boldsymbolμ)'$-almost Kenmotsu manifolds and finally, we construct an example. |
| title | Conformal vector fields on almost Kenmotsu manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2402.01425 |