Hiuri Reis

On gradient $ρ$-Einstein solitons with Bach tensor radially nonnegative

In this paper, we study $n$-dimensional gradient $ρ$-Einstein solitons whose Bach tensor is radially nonnegative. Under this assumption, we show that such $ρ$-Einstein solitons are locally warped products of an interval and an Einstein manifold, provided either $ρ\neq0$ or $ρ=0$ and the soliton is rectifiable. We obtain as a consequence that these solitons must have harmonic Weyl tensor and vanishing Bach tensor. We also finish the classification of complete locally conformally flat steady $ρ$-Einstein solitons and classify these manifolds when their Bach tensor is radially nonnegative and $n\in\{3,4\}$.