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

Abstract

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

References in corpus (1)

• Ricci flow on Kähler-Einstein manifolds

Cited by in corpus (10)

• Kahler-Ricci flow on stable Fano manifolds
• The modified Kähler-Ricci flow and solitons
• Kähler Ricci flow on Fano manifolds with vanished Futaki invariants
• Kähler-Ricci solitons on horospherical variety
• Multiplier ideal sheaves and the Kähler-Ricci flow on toric Fano manifolds with large symmetry
• Kähler-Ricci flow on homogeneous toric bundles
• Hirzebruch manifolds and positive holomorphic sectional curvature
• Some Type I solutions of Ricci flow with rotational symmetry
• On Feldman-Ilmanen-Knopf conjecture for the blow-up behavior of the Kahler Ricci flow
• Kähler Ricci flow with vanished Futaki invariant