Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\ast$-Ricci-Yamabe Soliton and Contact Geometry   It is well known that a unit sphere admits Sasakian 3-structure. Also,
Sasakian manifolds are locally isometric to a unit sphere under several
curvature and critical conditions. So, a natural question is: Does there exist
any curvature or critical condition under which a Sasakian 3-manifold
represents a geometrical object other than the unit sphere? In this regard, as
an extension of the $\ast$-Ricci soliton, the notion of $\ast$-Ricci-Yamabe
soliton is introduced and studied on two classes contact metric manifolds. A
$(2n + 1)$-dimensional non-Sasakian $N(k)$-contact metric manifold admitting
$\ast$-Ricci-Yamabe soliton is completely classified. Further, it is proved
that if a Sasakian 3-manifold $M$ admits $\ast$-Ricci-Yamabe soliton
$(g,V,\lambda,\alpha,\beta)$ under certain conditions on the soliton vector
field $V$, then $M$ is $\ast$-Ricci flat, positive Sasakian and the transverse
geometry of $M$ is Fano. In addition, the Sasakian 3-metric $g$ is homothetic
to a Berger sphere and the soliton is steady. Also, the potential vector field
$V$ is an infinitesimal automorphism of the contact metric structure.

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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: supr-con