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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.
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S. Brendle, Uniqueness of gradient Ricci solitons
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Bryant, R., unpublished work
Cited in the paper.
Cao, H.-D, Chen Qiang. On Locally Conformally Flat gradient Steady Ricci Solitons
Cited in the paper.
B.Kotschwar, On rotationally invariant shrinking gradient Ricci solitons ,
Cited in the paper.
A.Naber, Noncompact Shrinking 4-Solitons with Nonnegative Curvature,
Cited in the paper.
L.Ni and N.Wallach, On a classification of the gradient shrinking solitons,
Cited in the paper.
G.Perelman, The entropy formula for the Ricci flow and its geometric applications,
Cited in the paper.