On a classification of the gradient shrinking solitons

Abstract

The main purpose of this article is to provide an alternate proof to a result of Perelman on gradient shrinking solitons. In dimension three we also generalize the result by removing the $\kappa$-non-collapsing assumption. In high dimension this new method allows us to prove a classification result on gradient shrinking solitons with vanishing Weyl curvature tensor, which includes the rotationally symmetric ones.

References in corpus (3)

• Ricci flow with surgery on three-manifolds
• Ricci Flow and the Poincare Conjecture
• On rotationally invariant shrinking gradient Ricci solitons

Cited by in corpus (7)

• Recent Progress on Ricci Solitons
• On Bach-flat gradient shrinking Ricci solitons
• Geometry of Complete Gradient Shrinking Ricci Solitons
• Some characterizations of $\rho$-Einstein solitons
• Reduced distance based at singular time in the Ricci flow
• Rigidity of Complete Gradient Steady Ricci Solitons with Harmonic Weyl Curvature
• Commutator formulas for gradient Ricci shrinker and their application to linear stability