Notes on m-quasi Yamabe gradient solitons

We derive a divergence formula for an m-quasi Yamabe gradient soliton with finite m, and use it to give a short proof of the result “A compact m-quasi Yamabe gradient soliton \((M^n,g)\) $(M^n,g)$ , \(n\ge 3\) $n\ge 3$ , with finite m, has constant scalar curvature”. We also show that an m-quasi Yamabe gradient soliton with finite m and positive scalar curvature, whose soliton vector field leaves the Ricci tensor invariant, is shrinking and has constant scalar curvature.