Rigidity Theorem for integral pinched shrinking Ricci solitons

Abstract

We prove that an $n$-dimensional, $n\ge 4$, compact gradient shrinking Ricci soliton satisfying a $L^{\frac{n}{2}}$-pinching condition is isometric to a quotient of the round ${\mathbb{S}}^n$, which improves the rigidity theorem given by G. Catino (arXiv:1509.07416vl).

arXiv admin note: text overlap with arXiv:1509.07416 by other authors

References in corpus (1)

• Positively curved shrinking Ricci solitons are compact

Cited by in corpus (4)

• Rigidity theorems for compact Bach-flat manifolds with positive constant scalar curvature
• Rigidity of Riemannian manifolds with positive scalar curvature
• On compact manifolds with harmonic curvature and positive scalar curvature
• Some $L^p$ rigidity results for complete manifolds with harmonic curvature