Characterization of q-solitons under trace conditions and conformal vector fields

Abstract

We investigate gradient q-solitons $(M,g,f)$ characterized by a non-positive or non-negative trace of the structure tensor q. Through the imposition of specific regularity conditions on the potential function f, we deduce that M is both stationary and q-flat, consequently rendering it trivial. In the non-gradient case, we assume a contracted Bianchi type condition and prove certain characterizations of q-solitons $(M,g,X)$ when the vector field X is conformal. Our results showcase versatility as we apply them to solitons associated with diverse geometric flows.