English

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.

Keywords

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

R2 v1 2026-06-28T07:20:14.765Z