Existence of cohomogeneity one Einstein metrics

Abstract

This paper derives a sufficient condition for the existence of cohomogeneity one Einstein metrics on double disk bundles of two summands type. The condition is an inequality that involves geometric data from the principal orbits.

arXiv commentThe previous version has been split into several focused manuscripts. This version, with a different title, is one of them. The remaining results (the non-existence theorem and examples) have been separated and will be released as distinct manuscripts soon. We appreciate the valuable feedback from our readers. This is an accepted manuscript