Isometries on almost Ricci–Yamabe solitons

The purpose of the present paper is to examine the isometries of almost Ricci–Yamabe solitons. Firstly, the conditions under which a compact gradient almost Ricci–Yamabe soliton is isometric to Euclidean sphere \(S^n(r)\) are obtained. Moreover, we have shown that the potential f of a compact gradient almost Ricci–Yamabe soliton agrees with the Hodge–de Rham potential h. Next, we studied complete gradient almost Ricci–Yamabe soliton with \(\alpha \ne 0\) and non-trivial conformal vector field with non-negative scalar curvature and proved that it is either isometric to Euclidean space \(E^n\) or Euclidean sphere \(S^n.\) Also, solenoidal and torse-forming vector fields are considered. Lastly, some non-trivial examples are constructed to verify the obtained results.