We consider a smooth metric measure space (M, g, e −f dv). Let Δ f be its weighted Laplacian. Assuming that λ1(Δ f ) is positive and the m-dimensional Bakry-Émery curvature is bounded below in terms of λ1(Δ f ), we prove a splitting theorem for (M, g, e −f dv). This theorem generalizes previous results by Lam and Li-Wang (Trans Am Math Soc 362:5043–5062, 2010; J Diff Geom 58:501–534, 2001; see also J Diff Geom 62:143–162, 2002).
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机译：我们考虑一个光滑的度量度量空间（M，g，e -f dv）。令Δ f 为其加权拉普拉斯算子。假设λ 1 （Δ f ）为正，并且m维Bakry-Émery曲率在下面以λ 1 （Δ f ），我们证明了（M，g，e -f dv）的分裂定理。该定理概括了Lam和Li-Wang的先前结果（Trans Am Math Soc 362：5043-5062，2010； J Diff Geom 58：501-534，2001；另请参见J Diff Geom 62：143-162，2002）。
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