Rigidity of bach-flat gradient schouten solitons

In this paper, we show that complete Bach-flat Schouten solitons with \(n\ge 4\) $n\ge 4$ are rigid. When \(n=3\) $n=3$ we are able to conclude rigidity under a more general condition, namely when the Bach tensor is divergence-free. These results imply rigidity of locally conformally flat Schouten solitons for \(n\ge 3\) $n\ge 3$ .