A note on rigidity of the almost Ricci soliton |
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Authors: | Abdênago Barros José N Gomes Ernani Ribeiro Jr |
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Institution: | 1. Departamento de Matemática, Universidade Federal do Ceará, 60455-760, Fortaleza, CE, Brazil 2. Departamento de Matemática, Universidade Federal do Amazonas, 69077-070, Manaus, AM, Brazil
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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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