Article

K\"ahler-Ricci flow on a toric manifold with positive first Chern class

04/2007;
Source: arXiv

ABSTRACT 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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