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In this paper we prove that on a complete smooth metric measure space withnon-negative Bakry-\'Emery-Ricci curvature if the space of weighted L^2harmonic one-forms is non-trivial then the weighted volume of the manifold isfinite and universal cover of the manifold splits isometrically as the productof the real line with an hypersurface.

Harmonic Forms on Manifolds with Non-Negative Bakry-\'Emery-Ricci Curvature