Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost Kenmotsu metric as Ricci-Yamabe soliton   The object of the present paper is to characterize two classes of almost
Kenmotsu manifolds admitting Ricci-Yamabe soliton. It is shown that a
$(k,\mu)'$-almost Kenmotsu manifold admitting a Ricci-Yamabe soliton or
gradient Ricci-Yamabe soliton is locally isometric to the Riemannian product
$\mathbb{H}^{n+1}(-4) \times \mathbb{R}^n$. For the later case, the potential
vector field is pointwise collinear with the Reeb vector field. Also, a
$(k,\mu)$-almost Kenmotsu manifold admitting certain Ricci-Yamabe soliton with
the curvature property $Q \cdot P = 0$ is locally isometric to the hyperbolic
space $\mathbb{H}^{2n+1}(-1)$ and the non-existense of the curvature property
$Q \cdot R = 0$ is proved.

9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: alg-geom