English

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 GG-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}
}
R2 v1 2026-06-24T05:31:54.882Z