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.