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A splitting theorem on smooth metric measure spaces

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Abstract

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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  1. Nguyen Thac Dung

    Present address: Department of Mathematics, National Tsinghua University, No. 101, sec. 2, Kuang fu Road, Hsinchu, Taiwan

Authors and Affiliations

  1. Department of Mathematics, National University of Civil Engineering, No. 55, Giai Phong Road, Hanoi, Vietnam

    Nguyen Thac Dung

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  1. Nguyen Thac Dung
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Correspondence to Nguyen Thac Dung.

Additional information

The author was partially supported by the grant NAFOSTED 101.01-2011.13.

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Dung, N.T. A splitting theorem on smooth metric measure spaces. Arch. Math. 99, 179–187 (2012). https://doi.org/10.1007/s00013-012-0420-0

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