Integral pinched gradient shrinking ρ-Einstein solitons

The gradient shrinking ρ-Einstein soliton is a triple (Mn,g,f) such thatRij+fij=(ρR+λ)gij, where (Mn,g) is a Riemannian manifold, λ>0, ρ∈R∖{0} and f is the potential function on Mn. In this paper, using algebraic curvature estimates and the Yamabe-Sobolev inequality, we prove some integral pinching rigidity results for compact gradient shrinking ρ-Einstein solitons.