Triviality results for quasi $k$-Yamabe solitons

Abstract

In this paper, we show that any compact quasi k-Yamabe gradient solitons must have constant σ 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.