Ricci flows and bracket flows on twisted principal bundles

We show that Ricci flows of invariant metrics on twisted principal bundles with nilpotent fibres over \(S^1\) are immortal and type III. After normalisation and lift to the universal cover, a sequence of metrics converges in the Cheeger--Gromov topology to a homogeneous expanding Ricci soliton. The proof extends the bracket flow technique from homogeneous Ricci flows to invariant Ricci flows on twisted principal bundles.

Authors

Publication Details

Journal
arXiv (Cornell University)
Published
2026-11-02
DOI
https://doi.org/10.48550/arxiv.2611.02477
Primary Topic
Geometric Analysis and Curvature Flows
Type
preprint
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preprint

Ricci flows and bracket flows on twisted principal bundles

Henry Wood
arXiv (Cornell University)
Geometric Analysis and Curvature Flows
preprint

Ricci flows and bracket flows on twisted principal bundles

Henry Wood
preprint en

Abstract

We show that Ricci flows of invariant metrics on twisted principal bundles with nilpotent fibres over \(S^1\) are immortal and type III. After normalisation and lift to the universal cover, a sequence of metrics converges in the Cheeger--Gromov topology to a homogeneous expanding Ricci soliton. The proof extends the bracket flow technique from homogeneous Ricci flows to invariant Ricci flows on twisted principal bundles.

arXiv (Cornell University)
Geometric Analysis and Curvature Flows
DOIOpen Access PDFOpenAlex
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Ricci flows and bracket flows on twisted principal bundles — Henry Wood · arXiv (Cornell University) (2026) | TGRS Research Map | TGRS