On Locally Conformally Flat Gradient Steady Ricci Solitons

Neste trabalho apresentamos um estudo dos sólitons de Ricci gradiente steady localmente conformemente flat, baseado no trabalho de Huai-Dong Cao e Qiang Chen, onde são classificados os sólitons de Ricci gradiente steady n-dimensionais (n ≥ 3), completos, não-compactos e localmente conformemente flat. Em particular provamos que um sóliton de Ricci gradiente steady completo, não-compacto, não-flat e localmente conformemente flat é, a menos de homotetia, o sóliton de Bryant.In this work we present a study on locally conformally flat gradient steady Ricci solitons which is based on a Huai Dong-Cao and Qing Chen’s article, where they was classified the n-dimensional (n ≥ 3) complete noncompact locally conformally flat gradient steady Ricci solitons. In particular, we prove that a complete noncompact non-flat locally conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton