Certain classification of almost Ricci-Bourguignon solitons in three-dimensional almost $\alpha$-cosymplectic manifolds

Abstract We classify almost Ricci–Bourguignon solitons on three-dimensional almost $\alpha$ -cosymplectic manifolds. We study almost Ricci-Bourguignon solitons on almost $\alpha$ -cosymplectic manifolds, with an emphasis on their classification and geometric properties. Key results include soliton type characterization (shrinking, steady, expanding) via the parameter $\rho$ and conditions under which these solitons become Einstein. We also show that Ricci semi-symmetric manifolds with $\eta$ -parallel tensors reduce to almost cosymplectic structures. A five-dimensional example of an almost contact manifold admitting a Ricci-Bourguignon soliton has been constructed. Also, Lie-group classifications in dimension three are obtained, which are almost RB transversal solitons on almost $\alpha$ -cosymplectic manifolds.