Some results on [formula omitted]-almost Ricci solitons

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The purpose of this paper is to investigate some equations of structure for h-almost Ricci soliton which are a natural generalization for almost Ricci solitons. As a result we obtain that a compact nontrivial h-almost Ricci soliton is isometric to a Euclidean sphere with some conditions using the Hodge–de Rham decomposition theorem. Moreover, we acquire an integral formula for the compact h-almost Ricci solitons.