On the convergence of the Sasaki-Ricci flow

TL;DR

This paper proves that the Sasaki-Ricci flow on a Sasaki manifold converges exponentially fast to a Sasaki-Einstein metric under certain symmetry conditions.

Contribution

It establishes exponential convergence of the Sasaki-Ricci flow to Sasaki-Einstein metrics assuming trivial automorphism group.

Findings

Flow converges exponentially fast to Sasaki-Einstein metric

Convergence proven under trivial automorphism group condition

Provides conditions for existence and uniqueness of Sasaki-Einstein metrics

Abstract

Given a Sasaki manifold S, we prove the Sasaki-Ricci flow converges exponentially fast to a Sasaki-Einstein metric if one exists, provided the automorphism group of the transverse holomorphic structure is trivial.