A splitting theorem on smooth metric measure spaces |
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| Authors: | Nguyen Thac Dung |
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| Institution: | 1. Department of Mathematics, National University of Civil Engineering, No. 55, Giai Phong Road, Hanoi, Vietnam
2. Department of Mathematics, National Tsinghua University, No. 101, sec. 2, Kuang fu Road, Hsinchu, Taiwan
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| Abstract: | We consider a smooth metric measure space (M, g, e ?f dv). Let ?? f be its weighted Laplacian. Assuming that ??1(?? f ) is positive and the m-dimensional Bakry-émery curvature is bounded below in terms of ??1(?? 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?C5062, 2010; J Diff Geom 58:501?C534, 2001; see also J Diff Geom 62:143?C162, 2002). |
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