Strongly Hermitian Einstein-Maxwell Solutions on Ruled Surfaces
Abstract
This paper produces explicit strongly Hermitian Einstein-Maxwell solutions on the smooth compact -manifolds that are -bundles over compact Riemann surfaces of any genus. This generalizes the existence results by C. LeBrun in arXiv:1411.3992 and arXiv:1504.06669. Moreover, by calculating the (normalized) Einstein-Hilbert functional of our examples we generalize Theorem E of arXiv:1504.06669, which speaks to the abundance of Hermitian Einstein-Maxwell solutions on such manifolds. As a bonus, we exhibit certain pairs of strongly Hermitian Einstein-Maxwell solutions, first found in arXiv:1504.06669, on the first Hirzebruch surface in a form which clearly shows that they are conformal to a common K\"ahler metric. In particular, this yields a non-trivial example of non-uniqueness of positive constant scalar curvature metrics in a given conformal class.
Cite
@article{arxiv.1511.06805,
title = {Strongly Hermitian Einstein-Maxwell Solutions on Ruled Surfaces},
author = {Caner Koca and Christina W. Tønnesen-Friedman},
journal= {arXiv preprint arXiv:1511.06805},
year = {2016}
}
Comments
23 pages. An addendum section is added in regard to the recent results by V. Apostolov and G. Maschler