Bounding sectional curvature along a Kähler-Ricci flow

Details Bounding sectional curvature along a Kähler-Ricci flow Bounding sectional curvature along a Kähler-Ricci flow

2007-10-22

arxiv.org/abs/0710.3919v2

Mathematics

Differential Geometry

Scientific paper

If a normalized K\"{a}hler-Ricci flow $g(t),t\in[0,\infty),$ on a compact K\"{a}hler $n$-manifold, $n\geq 3$, of positive first Chern class satisfies $g(t)\in 2\pi c_{1}(M)$ and has $L^{n}$ curvature operator uniformly bounded, then the curvature operator will also uniformly bounded along the flow. Consequently the flow will converge along a subsequence to a K\"{a}hler-Ricci soliton.

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