Kahler-Ricci Flow on Projective Bundles over Kahler-Einstein Manifolds

Frederick Tsz-Ho Fong HKUST

Differential Geometry mathscidoc:1703.10005

Trans. Amer. Math. Soc., 366, (2), 563-589, 2014.2
We study the Kahler-Ricci flow on a class of projective bundles over a compact Kahler-Einstein manifold. Assuming the initial Kahler metric admits a U(1)-invariant momentum profile, we give a criterion, characterized by the triple (Σ,L,[ω0]), under which the P1-fiber collapses along the Kahler-Ricci flow and the projective bundle converges to Σ in the Gromov-Hausdorff sense. Furthermore, the Kahler-Ricci flow must have Type I singularity and is of (Cn ×P1)-type. This generalizes and extends part of Song-Weinkove’s work on Hirzebruch surfaces.
Kahler-Ricci flow, projective bundles, Type I singularity
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  title={Kahler-Ricci Flow on Projective Bundles over Kahler-Einstein Manifolds},
  author={Frederick Tsz-Ho Fong},
  booktitle={Trans. Amer. Math. Soc.},
Frederick Tsz-Ho Fong. Kahler-Ricci Flow on Projective Bundles over Kahler-Einstein Manifolds. 2014. Vol. 366. In Trans. Amer. Math. Soc.. pp.563-589. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170312221835208646662.
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