On locally conformally flat gradient steady Ricci solitons
On locally conformally flat gradient steady Ricci solitons
In this paper, we classify $n$-dimensional ($n\geq 3$) complete noncompact locally conformally flat gradient steady solitons. In particular, we prove that a complete noncompact nonflat locally conformally flat gradient steady Ricci soliton is, up to scaling, the Bryant soliton.