Ricci Flow on Torus Bundles
Differential Geometry
2021-08-31 v1
Abstract
In this paper we compute the Ricci flow formulas for invariant metrics on prinicpal -bundles compatible with the connection. Our primary focus is on torus bundles which we use to study a notion of Bakry-\'Emery Ricci flow as well as Ricci flow on circle bundles over K\"ahler-Einstein manifolds. The latter application gives us solutions to Ricci flows on Heisenberg groups and implicit solutions to Ricci flows on Berger 3-spheres and several other 3-dimensional manifolds.
Keywords
Cite
@article{arxiv.2108.13281,
title = {Ricci Flow on Torus Bundles},
author = {Dmytro Yeroshkin},
journal= {arXiv preprint arXiv:2108.13281},
year = {2021}
}