Some characterizations of almost *-Ricci-Bourguignon solitons

초록

The objective of this paper is to study an almost *-Ricci-Bourguignon soliton on paracontact geometry. It is shown that if the metric g of eta-Einstein para-Kenmotsu manifold (dim > 3) is almost *-Ricci-Bourguignon soliton, then M2n+1 is Einstein. Later, if g represents a gradient almost *-Ricci-Bourguignon soliton on a (2n + 1)-dimensional eta-Einstein para-Kenmotsu manifold then M2n+1 is either Einstein or there exists a vector field V is pointwise collinear with Reeb vector field xi. Next, for three-dimensional para-Kenmotsu manifold, it is a *-Ricci-Bourguignon soliton, then it is of constant curvature - 1. Finally, we prove that if the para-Sasakian metric is a *-Ricci-Bourguignon soliton on a manifold, then M2n+1 is either D-homothetic to an Einstein manifold, or the Ricci tensor of M2n+1 with respect to the canonical paracontact connection vanishes.

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