Generalized Kazdan-Warner equations on foliated manifolds
arXiv:2204.01253
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.
arXiv commentv3: References are added. Example 5 is corrected. v4: Some explanations are added. 7 pages. Comments are welcome