In this paper, we introduce a notion of compact m-quasi-Einstein manifolds \((M,g,X,\lambda )\) , possibly with non-empty boundary, where the potential vector field X is not necessarily a gradient. We prove that if X is Killing, then the scalar curvature S is constant. Conversely, if S is constant, X is Killing on the boundary, and the boundary of M is minimal, then X is Killing on M. Our results extend those of Bahuaud et al. [1], who proved an implication in the closed case under assumption \(m\ne -2\) , as well as the converse implication obtained by Cochran [10] (still assuming \(m\ne -2\) ) and Costa-Filho [12] without additional restrictions on m. Moreover, among other results, we derive a Chruściel-type inequality for compact m-quasi-Einstein manifolds with totally geodesic boundary, yielding a rigidity characterization in terms of boundary integrals.
