Abstract
Let (M, g) be a complete and connected Riemannian manifold of dimension n. By using the Bakry–Emery Ricci curvature tensor on M, we prove two theorems which correspond to the Myers compactness theorem.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Limoncu, M. The Bakry–Emery Ricci tensor and its applications to some compactness theorems. Math. Z. 271, 715–722 (2012). https://doi.org/10.1007/s00209-011-0886-7
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DOI: https://doi.org/10.1007/s00209-011-0886-7