Triviality results for quasi \(k\)-Yamabe solitons

In this paper, we show that any compact quasi \(k\)-Yamabe gradient solitons must have constant \(\sigma_{k}\)-curvature. Moreover, we provide a certain condition for a compact quasi \(k\)-Yamabe soliton to be gradient, and for noncompact solitons, we present a geometric rigidity under a decaiment condition on the norm of the soliton field.