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

Cited by in corpus (3)

• On Bach-flat gradient shrinking Ricci solitons
• On a classification of the quasi Yamabe gradient solitons
• Berger curvature decomposition, Weitzenböck formula, and canonical metrics on four-manifolds