Some rigidity results on <i>q</i>-solitons

Abstract We obtain rigidity and triviality results for q -solitons, assuming that the structure tensor q satisfies a condition analogous to the twice contracted second Bianchi identity (in particular, divergence free and trace free) and that the soliton vector field is projective and an infinitesimal harmonic transformation. In particular, the efficacy of our general results is manifested by applying it to Bach solitons. Finally, we generalize the evolution equation for the scalar curvature of Ricci solitons to q -solitons in order to recover the Bourguignon–Ezin formula and a rigidity result on compact Ricci solitons.