Coupled K\"ahler-Einstein and Hermitian-Yang-Mills equations

DOI10.1016/J.BULSCI.2023.103232arXiv2212.01043MaRDI QIDQ6419308

Publication date: 2 December 2022

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.

Mathematics Subject Classification ID

Global differential geometry of Hermitian and Kählerian manifolds (53C55) Local differential geometry of Hermitian and Kählerian structures (53B35) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Differential invariants (local theory), geometric objects (53A55)

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