Robustness of CSC Sasaki existence under the join operation

TL;DR

This paper investigates the existence of constant scalar curvature Sasaki metrics in the join of two regular Sasaki manifolds and explores cases of continuous families of extremal Sasaki twins.

Contribution

It extends the understanding of Sasaki geometry by analyzing the existence of special metrics in joined manifolds and introduces new cases of extremal Sasaki twins.

Findings

Existence conditions for CSC Sasaki metrics in join constructions

Identification of continuous families of extremal Sasaki twins

Insights into the structure of the Sasaki cone in joined manifolds

Abstract

The main purpose of this work is to explore the existence of constant scalar curvature Sasaki metrics in the Sasaki cone of the join of two regular Sasaki manifolds, $M_1$ and $M_2$. Furthermore, we consider some cases of continuous families of extremal Sasaki twins.