Smooth Quasi--Einstein Lifts of Locally Embeddable Three-Dimensional CR Manifolds

We prove a $C^\infty$ analogue of the real-analytic quasi--Einstein lifting theorem of Hill, Lewandowski and Nurowski \cite[Theorem~2.5]{HLN2008}. Every smooth, locally CR-embeddable, strictly pseudoconvex three-dimensional CR manifold admits, for each real cosmological constant, a local smooth Lore