Sasaki-Ricci flow equation on five-dimensional Sasaki-Einstein space $Y^{p,q}$

TL;DR

This paper studies the Sasaki-Ricci flow on five-dimensional Sasaki-Einstein spaces, producing explicit solutions that generate new Sasaki structures and analyzing their properties.

Contribution

It provides explicit solutions to the transverse Kähler-Ricci flow on $Y^{p,q}$ spaces, revealing new Sasaki structures and conditions for preserving Einstein properties.

Findings

Explicit solutions for the flow on $Y^{p,q}$ spaces.

Deformed metrics remain Sasaki but lose Einstein property.

Solutions can preserve or alter the transverse metric.

Abstract

We analyze the transverse K\"{a}hler-Ricci flow equation on Sasaki-Ein\-stein space $Y^{p,q}$. Explicit solutions are produced representing new five-dimensional Sasaki structures. Solutions which do not modify the transverse metric preserve the Sasaki-Einstein feature of the contact structure. If the transverse metric is altered, the deformed metrics remain Sasaki, but not Einstein.