Complete gradient shrinking Ricci solitons with pinched curvature

Abstract

We prove that any $n$--dimensional complete gradient Ricci soliton with pinched Weyl curvature is a finite quotient of $\RR^{n}$, $\RR \times \SS^{n-1}$ or $\SS^{n}$. In particular, we do not need to assume the metric to be locally conformally flat.

References in corpus (1)

• Remarks on non-compact gradient Ricci solitons