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 -polystability.
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