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Rigidity Results for Shrinking and Expanding Ricci Solitons

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Abstract

This paper proves some rigidity results for shrinking and expanding Ricci solitons. First, we demonstrate that compact shrinking Ricci solitons are Einstein if we control the maximum value of the potential function. Then, we prove some rigidity results for non-compact gradient expanding and shrinking Ricci solitons with pinched Ricci (or scalar) curvature, assuming an asymptotic condition on the scalar curvature at infinity.

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Acknowledgements

We would like to express our gratitude to Professor E. Ribeiro Jr. for his valuable contributions to the computations related to \(\mathbb{C}\mathbb{P}2\#(-\mathbb{C}\mathbb{P}2)\).

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  1. Universidade Federal de Goiás, IME, Caixa Postal 131, Goiânia, GO, CEP 74690-900, Brazil

    B. Leandro & J. Poveda

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  1. B. Leandro
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  2. J. Poveda
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Correspondence to B. Leandro.

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Benedito Leandro was partially supported by CNPq/Brazil Grants 303157/2022-4 and 403349/2021-4. Jeferson Poveda was supported by PROPG-CAPES [Finance Code 001].

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Leandro, B., Poveda, J. Rigidity Results for Shrinking and Expanding Ricci Solitons. J Geom Anal 33, 306 (2023). https://doi.org/10.1007/s12220-023-01372-0

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