A note on compactness theorems for the Bakry-Émery Ricci tensor and generalized quasi-Einstein tensors. (English) Zbl 1476.53061
Summary: In this paper, we extend compactness theorems of Cheeger, Gromov, Taylor, and Sprouse to the Bakry-Émery Ricci tensor and generalized quasi-Einstein tensors. Our results generalize previous results obtained by Yun and Wan.
MSC:
| 53C20 | Global Riemannian geometry, including pinching |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
Keywords:
Myers theorem; Bakry-Émery Ricci tensor; generalized quasi-Einstein tensor; mean curvature comparison; diameter estimateReferences:
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