Abstract
In this paper, we first focus on conformally flat almost \({C(\alpha)}\)-manifolds. Moreover, we construct an example of a 3-dimensional conformally flat almost \({\alpha}\)-Kenmotsu manifold which is of non-constant sectional curvature. By means of this example, we also illustrate a 3-dimensional conformally flat almost Kenmotsu manifold which not only contrasts with both H 3(−1) and \({H^{2}(-4)\times\mathbb{R}}\) but also is of non-constant sectional curvature. Then, we study conformally flat, \({\phi}\)-RK contact metric and almost contact metric manifolds. Next, we investigate the curvature properties of conformally flat generalized Sasakian space forms. Finally, we deal with conformally flat almost contact metric manifolds which are *-\({\eta}\)-Einstein. In this regard, we are also interested in conformally flat contact metric manifolds of \({{\rm dim}{\geq}5}\) which are *-\({\eta}\)-Einstein.
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This article was updated on January 13, 2016 because of a production error.
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Blair, D.E., Yıldırım, H. On Conformally Flat Almost Contact Metric Manifolds. Mediterr. J. Math. 13, 2759–2770 (2016). https://doi.org/10.1007/s00009-015-0652-x
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DOI: https://doi.org/10.1007/s00009-015-0652-x