Some characterizations of almost ∗-Ricci–Bourguignon solitons

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The objective of this paper is to study an almost ∗-Ricci–Bourguignon soliton on paracontact geometry. It is shown that if the metric [Formula: see text] of [Formula: see text]-Einstein para-Kenmotsu manifold (dim [Formula: see text]) is almost ∗-Ricci–Bourguignon soliton, then [Formula: see text] is Einstein. Later, if [Formula: see text] represents a gradient almost ∗-Ricci–Bourguignon soliton on a [Formula: see text]-dimensional [Formula: see text]-Einstein para-Kenmotsu manifold then [Formula: see text] is either Einstein or there exists a vector field [Formula: see text] is pointwise collinear with Reeb vector field [Formula: see text]. Next, for three-dimensional para-Kenmotsu manifold, it is a ∗-Ricci–Bourguignon soliton, then it is of constant curvature [Formula: see text]. Finally, we prove that if the para-Sasakian metric is a ∗-Ricci–Bourguignon soliton on a manifold, then [Formula: see text] is either [Formula: see text]-homothetic to an Einstein manifold, or the Ricci tensor of [Formula: see text] with respect to the canonical paracontact connection vanishes.