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A note on rigidity of the almost Ricci soliton

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Abstract

The aim of this paper is to prove that a gradient almost Ricci soliton \({(M^{n}, g, \nabla f, \lambda )}\) whose Ricci tensor is Codazzi has constant sectional curvature. In particular, in the compact case, we deduce that (M n, g) is isometric to a Euclidean sphere and f is a height function. Moreover, we also classify gradient almost Ricci solitons with constant scalar curvature R provided a suitable function achieves a maximum in M n.

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Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal do Ceará, 60455-760, Fortaleza, CE, Brazil

    Abdênago Barros & Ernani Ribeiro Jr.

  2. Departamento de Matemática, Universidade Federal do Amazonas, 69077-070, Manaus, AM, Brazil

    José N. Gomes

Authors
  1. Abdênago Barros
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  2. José N. Gomes
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  3. Ernani Ribeiro Jr.
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Corresponding author

Correspondence to Ernani Ribeiro Jr..

Additional information

Dedicated to Professor J. L. Barbosa on the occasion of his 70th birthday

A. Barros was partially supported by CNPq-Brazil.

J. N. Gomes was partially supported by CNPq-Brazil and FAPEAM-Brazil.

E. Ribeiro was partially supported by Mathematics Research Fellowship at ICTP-Italy and FUNCAP-Brazil.

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Barros, A., Gomes, J.N. & Ribeiro, E. A note on rigidity of the almost Ricci soliton. Arch. Math. 100, 481–490 (2013). https://doi.org/10.1007/s00013-013-0524-1

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  • DOI: https://doi.org/10.1007/s00013-013-0524-1

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