In this paper, we consider complete smooth metric measure spaces \((M, d s_M^2, e^{-f} d v)\) that satisfy a weighted Poincaré inequality with a nonnegative weight function \(\rho \) and have Bakry–Émery curvature bounded from below in terms of \(\rho \) . In particular, we investigate the structure at infinity of this class of complete smooth metric measure spaces when \(\rho \) has either a zero or nonzero limit at infinity. Besides, if the weighted volume of M satisfies a growth condition, we prove a splitting type theorem for \(\left( M, ds_M^2, e^{-f} dv\right) \) .
