A note on rigidity of the almost Ricci soliton

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The aim of this paper is to prove that a gradient almost Ricci soliton \({(M^{n}, g, \nabla f, \lambda )}\) whose Ricci tensor is Codazzi has constant sectional curvature. In particular, in the compact case, we deduce that (Mn, g) is isometric to a Euclidean sphere and f is a height function. Moreover, we also classify gradient almost Ricci solitons with constant scalar curvature R provided a suitable function achieves a maximum in Mn.