English

Generalized Kazdan-Warner equations on foliated manifolds

Differential Geometry 2023-05-02 v4

Abstract

On compact foliated manifolds, we extend the theorem on the existence and uniqueness of solutions to generalized Kazdan-Warner equations. We provide examples of PDEs that we solve, including the transverse Hitchin equation for a diagonal harmonic metric on basic cyclic Higgs bundles over a 3-dimensional complex codimension one foliated manifold, and its generalizations.

Keywords

Cite

@article{arxiv.2204.01253,
  title  = {Generalized Kazdan-Warner equations on foliated manifolds},
  author = {Natsuo Miyatake},
  journal= {arXiv preprint arXiv:2204.01253},
  year   = {2023}
}

Comments

v3: References are added. Example 5 is corrected. v4: Some explanations are added. 7 pages. Comments are welcome

R2 v1 2026-06-24T10:36:29.568Z