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Rigidity Theorem for Integral Pinched Static Manifolds and Related Critical Spaces

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Abstract

The aim of this paper is to investigate positive static triples, critical metrics of volume functional, and critical metrics of the total scalar curvature functional satisfying a \(L^{n/2}\)-pinching condition.

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Acknowledgements

The first author was partially supported by PPP/FAPEPI/ MCT/CNPq, Brazil [Grant: 007/2018] and CNPq/Brazil [Grant: 422900/2021-4 and 302389/2022-9].

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  1. Departamento de Matemática, Universidade Federal do Piauí, Teresina, Piauí, 64049-550, Brazil

    H. Baltazar & C. Queiroz

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  1. H. Baltazar
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  2. C. Queiroz
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Correspondence to H. Baltazar.

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Baltazar, H., Queiroz, C. Rigidity Theorem for Integral Pinched Static Manifolds and Related Critical Spaces. J Geom Anal 34, 158 (2024). https://doi.org/10.1007/s12220-024-01603-y

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