Saved in:
Bibliographic Details
Main Author: Chi, Hanci
Format: Preprint
Published: 2022
Subjects:
Online Access:https://arxiv.org/abs/2210.13216
Tags: Add Tag
No Tags, Be the first to tag this record!
Table of Contents:
  • We prove that there exists at least one positive Einstein metric on $\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$ for $m\geq 2$. Based on the existence of the first Einstein metric, we give a criterion to check the existence of a second Einstein metric on $\mathbb{HP}^{m+1}\sharp \overline{\mathbb{HP}}^{m+1}$. We also investigate the existence of cohomogeneity one positive Einstein metrics on $\mathbb{S}^{4m+4}$ and prove the existence of a non-standard Einstein metric on $\mathbb{S}^8$.