The K\"ahler-Ricci flow with positive bisectional curvature

TL;DR

This paper proves that the K"ahler-Ricci flow on manifolds with positive first Chern class converges to a K"ahler-Einstein metric under positive bisectional curvature and stability assumptions.

Contribution

It establishes convergence of the K"ahler-Ricci flow to K"ahler-Einstein metrics with new conditions involving positive bisectional curvature.

Findings

Flow converges to K"ahler-Einstein metric under specified conditions

Positive bisectional curvature is key for convergence

Provides stability criteria for the flow

Abstract

We show that the K\"ahler-Ricci flow on a manifold with positive first Chern class converges to a K\"ahler-Einstein metric assuming positive bisectional curvature and certain stability conditions.