Certain results of κ-almost gradient Ricci-Bourguignon soliton on pseudo-Riemannian manifolds

Abstract

The prime object in this article is to study κ-almost Ricci-Bourguignon soliton and κ-almost gradient Ricci-Bourguignon soliton within the framework of paracontact metric manifolds. Here, we realize some conditions under which a paracontact metric manifold admitting a κ-Ricci–Bourguignon almost soliton is Einstein (trivial) and η-Einstein. We also show that if a three dimensional para-Kenmotsu manifold M3 admitting a κ-almost gradient Ricci-Bourguignon soliton with a constant scalar curvature, then the soliton becomes an almost gradient Ricci-Bourguignon soliton whose soliton function is −Ω. We also characterize and find some notable results κ-almost gradient Ricci-Bourguignon soliton on para-Sasakian manifolds and para-cosymplectic manifolds.