English

Coupled K\"ahler-Einstein metrics

Differential Geometry 2017-03-16 v2 Complex Variables

Abstract

We propose new types of canonical metrics on K\"ahler manifolds, called coupled K\"ahler-Einstein metrics, generalizing K\"ahler-Einstein metrics. We prove existence and uniqueness results in the cases when the canonical bundle is ample and when the manifold is K\"ahler-Einstein Fano. In the Fano case we also prove that existence of coupled K\"ahler-Einstein metrics imply a certain algebraic stability condition, generalizing KK-polystability.

Keywords

Cite

@article{arxiv.1608.07209,
  title  = {Coupled K\"ahler-Einstein metrics},
  author = {Jakob Hultgren and David Witt Nyström},
  journal= {arXiv preprint arXiv:1608.07209},
  year   = {2017}
}

Comments

18 pages

R2 v1 2026-06-22T15:30:59.962Z