Golden Riemannian Manifolds Admitting Ricci–Bourguignon Solitons

In this paper, we examine Ricci–Bourguignon solitons on locally decomposable golden Riemannian manifolds of constant golden sectional curvature. First, we establish an explicit expression for the soliton constant in terms of the golden structure and the Bourguignon parameter. Second, we explore the geometry of these solitons when the potential vector fields are Killing, conformal Killing, homothetic, or concurrent. Finally, we initiate the study of golden Ricci–Bourguignon solitons, determine their soliton constants, and examine their properties under the specific potential vector fields.