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Abstract

Let \((M^{2n+1},\phi ,\xi ,\eta ,g)\) be a non-Kenmotsu almost Kenmotsu \((k,\mu )'\)-manifold. If the metric g represents a Yamabe soliton, then either \(M^{2n+1}\) is locally isometric to the product space \(\mathbb {H}^{n+1}(-4)\times \mathbb {R}^n\) or \(\eta \) is a strict infinitesimal contact transformation. The later case can not occur if a Yamabe soliton is replaced by a gradient Yamabe soliton. Some corollaries of this theorem are given and an example illustrating this theorem is constructed.

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Acknowledgements

This work was supported by the Key Scientific Research Program in Universities of Henan Province (No. 20A110023) and the Fostering Foundation of National Foundation in Henan Normal University (No. 2019PL22). The author would like to thank the referees for their careful reading and many suggestions that improves the paper.

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Correspondence to Yaning Wang.

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Wang, Y. Almost Kenmotsu \((k,\mu )'\)-manifolds with Yamabe solitons. RACSAM 115, 14 (2021). https://doi.org/10.1007/s13398-020-00951-y

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