Coupled K\"ahler-Einstein and Hermitian-Yang-Mills equations
Differential Geometry
2022-12-20 v2 Symplectic Geometry
Abstract
We introduce a new system of equations coupling K\"ahler-Einstein and Hermitian-Yang-Mills equations. We provide a moment map interpretation of these equations. We identify a Futaki type invariant as an obstruction to the existence of solutions to these equations. We also prove a Matsushima-Lichnerowicz type theorem. We prove a deformation result that produces nontrivial solutions of these equations under some conditions. We produce examples on some projective bundles using Calabi ansatz.
Cite
@article{arxiv.2212.01043,
title = {Coupled K\"ahler-Einstein and Hermitian-Yang-Mills equations},
author = {Kartick Ghosh},
journal= {arXiv preprint arXiv:2212.01043},
year = {2022}
}
Comments
some minor changes, added section 3.2