Compact gradient shrinking ρ-Einstein solitons with pinching conditions

Abstract

We prove that an n-dimensional, n≥4, compact gradient shrinking ρ-Einstein soliton satisfying suitable pinching conditions and curvature conditions is isometric to a quotient of the round sphere Sn. Our results extend the rigidity theorems given by Huang (Integral pinched gradient shrinking ρ-Einstein solitons, 2017) in dimension 4≤n≤6.