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Critical point equation and closed conformal vector fields

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  • J. F. da Silva Filho

Abstract

In this article, we study the critical points of the total scalar curvature functional restricted to the space of metrics with constant scalar curvature of unitary volume, for simplicity, CPE metrics. Here, we prove that a CPE metric admitting a non‐trivial closed conformal vector field must be isometric to a round sphere metric, which provides a partial answer to the CPE conjecture.

Suggested Citation

  • J. F. da Silva Filho, 2020. "Critical point equation and closed conformal vector fields," Mathematische Nachrichten, Wiley Blackwell, vol. 293(12), pages 2299-2305, December.
    • Handle: RePEc:bla:mathna:v:293:y:2020:i:12:p:2299-2305
    DOI: 10.1002/mana.201900316
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    References listed on IDEAS

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    1. A. Barros & B. Leandro & E. Ribeiro Jr, 2015. "Critical metrics of the total scalar curvature functional on 4-manifolds," Mathematische Nachrichten, Wiley Blackwell, vol. 288(16), pages 1814-1821, November.
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    Cited by:

    1. Sharief Deshmukh & Nasser Bin Turki & Ramesh Sharma, 2024. "Characterizations of Spheres and Euclidean Spaces by Conformal Vector Fields," Mathematics, MDPI, vol. 12(20), pages 1-16, October.
    2. Hanan Alohali & Sharief Deshmukh & Bang-Yen Chen & Hemangi Madhusudan Shah, 2024. "Hodge Decomposition of Conformal Vector Fields on a Riemannian Manifold and Its Applications," Mathematics, MDPI, vol. 12(17), pages 1-14, August.

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