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.
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