Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $*$-Ricci solitons and gradient almost $*$-Ricci solitons on Kenmotsu
  manifolds   In this paper, we consider $*$-Ricci soliton in the frame-work of Kenmotsu
manifolds. First, we prove that if the metric of a Kenmotsu manifold $M$ is a
$*$-Ricci soliton, then soliton constant $\lambda$ is zero. For 3-dimensional
case, if $M$ admits a $*$-Ricci soliton, then we show that $M$ is of constant
sectional curvature -1. Next, we show that if $M$ admits a $*$-Ricci soliton
whose potential vector field is collinear with the characteristic vector field
$\xi$, then $M$ is Einstein and soliton vector field is equal to $\xi$.
Finally, we prove that if $g$ is a gradient almost $*$-Ricci soliton, then
either $M$ is Einstein or the potential vector field is collinear with the
characteristic vector field on an open set of $M$. We verify our result by
constructing examples for both $*$-Ricci soliton and gradient almost $*$-Ricci
soliton.

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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg