References & Citations
Mathematics > Differential Geometry
Title: Almost Kenmotsu Manifolds Admitting Certain Critical Metric
(Submitted on 28 Apr 2020 (v1), last revised 5 Apr 2021 (this version, v2))
Abstract: In the present paper, we introduce the notion of $\ast$-Miao-Tam critical equation on almost contact metric manifolds and studied on a class of almost Kenmotsu manifold. It is shown that if the metric of a $(2n + 1)$-dimensional $(k,\mu)'$-almost Kenmotsu manifold $(M,g)$ satisfies the $\ast$-Miao-Tam critical equation, then the manifold $(M,g)$ is $\ast$-Ricci flat and locally isometric to the Riemannian product of a $(n + 1)$-dimensional manifold of constant sectional curvature $-4$ and a flat $n$-dimensional manifold. Finally, an illustrative example is presented to support the main theorem.
Submission history
From: Dibakar Dey [view email][v1] Tue, 28 Apr 2020 10:20:39 GMT (8kb)
[v2] Mon, 5 Apr 2021 20:53:31 GMT (7kb)
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