Study Ricci flow on CP1-bundles over Kähler-Einstein manifolds.
problem Preserving an initial metric on CP1-bundles.
method Ricci flow on CP1-bundles over a product of Kähler-Einstein manifolds.
result The ansatz is preserved along the Ricci flow.
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Let (M,g) be a Riemannian 4-manifold. The twistor space Z->M is a CP1-bundle whose total space Z admits a natural metric h. The aim of this article is to study properties of complex structures on (Z,h) which are compatible with the CP1-fibration and the metric h. The results obtained enable us to translate some metric …