Triviality results for quasi $k$-Yamabe solitons

Abstract

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.

References in corpus (1)

• Rigidity results for quotient almost Yamabe solitons