Some Type I solutions of Ricci flow with rotational symmetry

Details Some Type I solutions of Ricci flow with rotational symmetry Some Type I solutions of Ricci flow with rotational symmetry

2012-03-13

arxiv.org/abs/1203.2688v1

Mathematics

Differential Geometry

Scientific paper

We prove that the Ricci flow on CP^n blown-up at one point starting with any rotationally symmetric Kahler metric must develop Type I singularities. In particular, if the total volume does not go to zero at the singular time, the parabolic blow-up limit of the Type I Ricci flow along the exceptional divisor is a complete non-flat shrinking gradient Kahler-Ricci soliton on a complete Kahler manifold homeomorphic to C^n blown-up at one point.

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