2021/08/30 by Dmytro Yeroshkin, Yeroshkin, Dmytro
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2108.13281
openalex publication_date 2021/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we compute the Ricci flow formulas for invariant metrics on prinicpal G-bundles compatible with the connection. Our primary focus is on torus bundles which we use to study a notion of Bakry-Émery Ricci flow as well as Ricci flow on circle bundles over Kähler-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.