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A note on compactness theorems for the Bakry–Émery Ricci tensor and generalized quasi-Einstein tensors

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Abstract

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.

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Acknowledgements

The author is very grateful to the referee for the valuable comments and suggestions.

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  1. Department of Mathematics, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul, Republic of Korea

    Sanghun Lee

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  1. Sanghun Lee
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Correspondence to Sanghun Lee.

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The author was supported by the National Research Foundation of Korea (NRF-2019R1A6A3A13096187)

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Lee, S. A note on compactness theorems for the Bakry–Émery Ricci tensor and generalized quasi-Einstein tensors. Arch. Math. 117, 469–480 (2021). https://doi.org/10.1007/s00013-021-01620-1

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  • DOI: https://doi.org/10.1007/s00013-021-01620-1

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