In this paper, we prove some rigidity theorems for compact Bach-flat $n$-manifold with the positive constant scalar curvature. In particular, our conditions in Theorem 2 have the additional properties of being sharp.
"Rigidity theorems for compact Bach-flat manifolds with positive constant scalar curvature." Hokkaido Math. J. 47 (3) 581 - 605, October 2018. https://doi.org/10.14492/hokmj/1537948832