Four-dimentional Gradient Shrinking Solitons with Positive Isotropic Curvature

Abstract

We show that a four-dimensional complete gradient shrinking Ricci soliton with positive isotropic curvature is either a quotient of S^4 or a quotient of S^3 cross R. This gives a clean classification result removing the earlier additional assumptions in [13] by Wallach and the second author.

arXiv comment9 pages, Any comments are welcome

References in corpus (1)

• Geometry of shrinking Ricci solitons

Cited by in corpus (5)

• Structure at infinity for shrinking Ricci solitons
• Ancient solutions to the Ricci flow with isotropic curvature conditions
• A uniqueness theorem for asymptotically cylindrical shrinking Ricci solitons
• The rigidity of ${\mathbb{S}}^3\times \mathbb{R}$ under ancient Ricci flow
• A compactness theorem for four-dimensional shrinking gradient Ricci solitons