Abstract
In this paper, by virtue of a system of partial differential equations, we give a necessary and sufficient condition for an almost Kenmotsu 3-manifold to be conformally flat. As an application, we obtain that an almost Kenmotsu 3-H-manifold with scalar curvature invariant along the Reeb vector field is conformally flat if and only if it is locally isometric to either the hyperbolic space \(\mathbb {H}^3(-1)\) or the Riemannian product \(\mathbb {H}^{2}(-4)\times \mathbb {R}\). Some concrete examples verifying main results are presented.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (No. 11526080), Key Scientific Research Program in Universities of Henan Province (No. 16A110004), the Research Foundation for the Doctoral Program of Henan Normal University (No. qd14145), and the Youth Science Foundation of Henan Normal University (No. 2014QK01).
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Wang, Y. Conformally Flat Almost Kenmotsu 3-Manifolds. Mediterr. J. Math. 14, 186 (2017). https://doi.org/10.1007/s00009-017-0984-9
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DOI: https://doi.org/10.1007/s00009-017-0984-9