Sasaki-Einstein metrics and K-stability
Differential Geometry
2019-06-05 v2
Abstract
We show that a polarized affine variety admits a Ricci flat K\"ahler cone metric, if and only if it is K-stable. This generalizes Chen-Donaldson-Sun's solution of the Yau-Tian-Donaldson conjecture to K\"ahler cones, or equivalently, Sasakian manifolds. As an application we show that the five-sphere admits infinitely many families of Sasaki-Einstein metrics.
Cite
@article{arxiv.1512.07213,
title = {Sasaki-Einstein metrics and K-stability},
author = {Tristan C. Collins and Gábor Székelyhidi},
journal= {arXiv preprint arXiv:1512.07213},
year = {2019}
}
Comments
v2: 64 pages, added proof of converse of main result