On the classification of Ricci solitons and Yamabe solitons
Nenhuma Miniatura disponível
Data
2023-03-20
Autores
Título da Revista
ISSN da Revista
Título de Volume
Editor
Universidade Federal de Goiás
Resumo
In this work, we will study the self-similar solutions of both Ricci flow and Yamabe flow.
These solutions are also known as Ricci and Yamabe soliton, respectively. Inspired by the
divergence equation used by Robinson in his demonstration of the uniqueness of static
black holes and by Brendle’s classification of steady Ricci solitons, we will make some
important characterizations of these solitons. We prove that four-dimensional gradient
Yamabe solitons must have a Yamabe metric, provided that an asymptotic condition holds.
Inspired by the geometry of the cigar soliton, we demonstrate that a gradient steady Ricci
soliton is either Ricci flat with a constant potential function or a quotient of the product
steady soliton N
n−1×R, where N
n−1
is Ricci flat, or isometric to the Bryant soliton. In the
final Chapter, we prove some rigidity results for shrinking and expanding Ricci solitons.
Descrição
Palavras-chave
Citação
CONTRERAS, J. A. P. On the classification of Ricci solitons and Yamabe solitons. 2023. 76 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2023.