Unicidade dos solitons de Ricci gradiente estáveis
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2022-11-18
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Universidade Federal de Goiás
Resumo
We present the Ricci solitons, objects that appear as self-similar solutions of the Ricci
flow. We show some properties and results related to these solitons. In addition, we study
[2] and prove that a three-dimensional gradient steady Ricci soliton that is asymptotic to
the Bryant soliton must be isometric to the Bryant soliton. This theorem was proved by
Brendle [1], and more generally stated by Cao et al. However Cao states the result without
any proof, thus, the ultimate goal of our research is to demonstrate the theorem stated by
Cao by generalizing Brendle’s result to dimensions greater than or equal to 3.
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SOUZA, V. E. R. Unicidade dos solitons de Ricci gradiente estáveis. 2022. 82 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2022.