  In this paper, we study vanishing and splitting results on a complete smooth
metric measure space $(M^n,g,\mathrm{e}^{-f}\mathrm{d}v)$ with various negative
$m$-Bakry-\'Emery-Ricci curvature lower bounds in terms of the first spectrum
$\lambda_1(\Delta_f)$ of the weighted Laplacian $\Delta_f$, i.e.
$\mathrm{Ric}_{m,n}\geq -a\lambda_1(\Delta_f)-b$ for $0<a\leq\dfrac{m}{m-1},
b\geq0$. In particular, we consider three main cases for different $a$ and $b$
with or without conditions on $\lambda_1(\Delta_f)$. These results are
extensions of Dung and Vieira, and weighted generalizations of Li-Wang,
Dung-Sung and Vieira.
