Non-existence of cohomogeneity one Einstein metrics of two summands
Differential Geometry
2025-05-13 v1
Abstract
We prove the non-existence of cohomogeneity one Einstein metrics on a class of compact manifolds arising as double disk bundles, whose principal orbits split into two inequivalent irreducible summands. The proof uses a phase space barrier argument that yields a new obstruction to the existence of closed cohomogeneity one Einstein metrics, even when the principal orbits admit homogeneous Einstein metrics.
Keywords
Cite
@article{arxiv.2505.06631,
title = {Non-existence of cohomogeneity one Einstein metrics of two summands},
author = {Hanci Chi},
journal= {arXiv preprint arXiv:2505.06631},
year = {2025}
}
Comments
This submission contains the non-existence result originally part of arXiv:2405.10836v3, now split off for clarity. We appreciate the valuable feedback from our readers