Invariant Einstein metrics on Ledger-Obata spaces

TL;DR

This paper classifies and estimates invariant Einstein metrics on Ledger-Obata spaces, providing a detailed analysis for specific cases and general estimates for broader classes.

Contribution

It offers a classification of invariant Einstein metrics on F^4/diag(F) and estimates their number on general Ledger-Obata spaces F^m/diag(F).

Findings

Classified invariant Einstein metrics on F^4/diag(F).

Estimated the number of such metrics on F^m/diag(F).

Provided insights into the structure of invariant Einstein metrics on Ledger-Obata spaces.

Abstract

In this paper, we study invariant Einstein metrics on Ledger-Obata spaces $F^m/\operatorname{diag}(F)$. In particular, we classify invariant Einstein metrics on $F^4/\operatorname{diag}(F)$ and estimate the number of invariant Einstein metrics on general Ledger-Obata spaces $F^{m}/\operatorname{diag}(F)$.