On four-dimensional anti-self-dual gradient Ricci solitons

Abstract

In this note we prove that any four-dimensional half conformally flat gradient steady Ricci soliton must be either Bryant's soliton or Ricci flat. We also classify four-dimensional half conformally flat gradient shrinking Ricci solitons with bounded curvature.

References in corpus (2)

• On rotationally invariant shrinking gradient Ricci solitons
• Uniqueness of gradient Ricci solitons