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

Abstract We classify almost Ricci–Bourguignon solitons on three-dimensional almost -cosymplectic manifolds. We study almost Ricci-Bourguignon solitons on almost -cosymplectic manifolds, with an emphasis on their classification and geometric properties. Key results include soliton type characterization (shrinking, steady, expanding) via the parameter and conditions under which these solitons become Einstein. We also show that Ricci semi-symmetric manifolds with -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 -cosymplectic manifolds.