Abstract
In this paper, first we consider that the conformal vector field X is identical with the Reeb vector field \(\varsigma \) and next, assume that X is pointwise collinear with the Reeb vector field \(\varsigma \); in both cases it is shown that the manifold \(N^{2m+1}\) becomes a Kenmotsu manifold and \(N^{2m+1}\) is locally a warped product \(N' \times _{f} M^{2m}\), in which \(M^{2m}\) indicate an almost Kähler manifold, with coordinate t, \(N'\) being the open interval and \(f = ce^{t}\) for some c ( positive constant). Beside these, we establish that if a \((k,\mu )'\)-almost Kenmotsu manifold admits a Killing vector field X, then either it is locally a warped product of an open interval and an almost Kähler manifold or X is a strict infinitesimal contact transformation. Furthermore, we also investigate \(\eta \)-Ricci-Yamabe soliton with conformal vector fields on \((k,\mu )'\)-almost Kenmotsu manifolds and finally, we construct two examples.
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Acknowledgements
We would like to thank the Referees and the Editor for reviewing the paper carefully and their valuable comments to improve the quality of the paper. Arpan Sardar is financially supported by UGC, Ref. ID. 4603/(CSIR-UGCNETJUNE2019).
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De, U.C., Sardar, A. & De, K. Conformal vector fields on almost Kenmotsu manifolds. Afr. Mat. 34, 72 (2023). https://doi.org/10.1007/s13370-023-01118-9
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DOI: https://doi.org/10.1007/s13370-023-01118-9
Keywords
- Conformal vector fields
- Infinitesimal strict contact transformation
- \(\eta \)-Ricci-Yamabe solitons
- Almost Kenmotsu manifolds
- \((k,\mu )'\)-almost Kenmotsu manifolds