Bach-flat gradient steady Ricci solitons

Abstract

In this paper we prove that any $n$-dimensional ($n\ge 4$) complete Bach-flat gradient steady Ricci soliton with positive Ricci curvature is isometric to the Bryant soliton. We also show that a three-dimensional gradient steady Ricci soliton with divergence-free Bach tensor is either flat or isometric to the Bryant soliton. In particular, these results improve the corresponding classification theorems for complete locally conformally flat gradient steady Ricci solitons in [6] and [9].

References in corpus (1)

• Recent Progress on Ricci Solitons

Cited by in corpus (7)

• On Bach-flat gradient shrinking Ricci solitons
• On the structure of gradient Yamabe solitons
• Rotational symmetry of Ricci solitons in higher dimensions
• On the geometry of gradient Einstein-type manifolds
• An asymptotically cusped three dimensional expanding gradient Ricci soliton
• Bach-flat Lie groups in dimension 4
• Ricci flow on cone surfaces and a three-dimensional expanding soliton