Destabilising compact warped product Einstein manifolds
Differential Geometry
2019-01-09 v3 Mathematical Physics
math.MP
Abstract
The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein metrics are unstable. By exploiting the relationship between warped product Einstein metrics, quasi-Einstein metrics and Ricci solitons, we introduce a new destabilising perturbation (the Ricci variation) and show that certain infinite families of warped product Einstein metrics will be unstable in high dimensions.
Keywords
Cite
@article{arxiv.1607.05766,
title = {Destabilising compact warped product Einstein manifolds},
author = {Wafaa Batat and Stuart James Hall and Thomas Murphy},
journal= {arXiv preprint arXiv:1607.05766},
year = {2019}
}
Comments
V3: Final Version. To appear in Comm. Anal. Geom