Triviality results for quasi k-Yamabe solitons

Abstract

In this paper, we show that any compact quasi k-Yamabe gradient soliton 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 decay condition on the norm of the soliton field.