Kähler-Ricci flow on a toric manifold with positive first Chern class

Details Kähler-Ricci flow on a toric manifold with positive first Chern class Kähler-Ricci flow on a toric manifold with positive first Chern class

2007-03-16

arxiv.org/abs/math/0703486v1

Mathematics

Differential Geometry

Scientific paper

In this note, we prove that on an $n$-dimensional compact toric manifold with positive first Chern class, the K\"ahler-Ricci flow with any initial $(S^1)^n$-invariant K\"ahler metric converges to a K\"ahler-Ricci soliton. In particular, we give another proof for the existence of K\"ahler-Ricci solitons on a compact toric manifold with positive first Chern class by using the K\"ahler-Ricci flow.

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