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PreprintCC BY-NC-ND 4.0arXiv

On the singularity formation of gauge fields coupled to Ricci flow

  • Andoni Royo Abrego
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Abstract

We study a family of coupled geometric evolution equations describing the deformation of a Riemannian metric and a non-abelian gauge field on closed manifolds, which generalizes the Ricci--Yang--Mills flow. We derive interior curvature estimates, find a preserved integral curvature condition, and discover a scaling invariant monotone functional analogue to Perelman's entropy. In particular, we prove strong dominance of the Riemannian curvature over the gauge curvature at finite-time singularities in all dimensions. We also provide a non-trivial explicit example of a shrinking self-similar solution on a SU(2) bundle over S4.

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Cite

BibTeXRIS
BibTeX
@misc{abrego2026singularity,
  title = {{On the singularity formation of gauge fields coupled to Ricci flow}},
  author = {Andoni Royo Abrego},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27644},
  eprint = {2609.27644},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27644},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On the singularity formation of gauge fields coupled to Ricci flow
AU  - Andoni Royo Abrego
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27644
UR  - https://arxiv.org/abs/2609.27644
AB  - We study a family of coupled geometric evolution equations describing the deformation of a Riemannian metric and a non-abelian gauge field on closed manifolds, which generalizes the Ricci--Yang--Mills flow. We derive interior curvature estimates, find a preserved integral curvature condition, and discover a scaling invariant monotone functional analogue to Perelman's entropy. In particular, we prove strong dominance of the Riemannian curvature over the gauge curvature at finite-time singularities in all dimensions. We also provide a non-trivial explicit example of a shrinking self-similar solution on a SU(2) bundle over S^4.
ER  -