Sasaki-Einstein metrics and K-stability
Abstract
We show that a polarized affine variety admits a Ricci flat Kähler cone metric, if and only if it is K-stable. This generalizes Chen-Donaldson-Sun's solution of the Yau-Tian-Donaldson conjecture to Kähler cones, or equivalently, Sasakian manifolds. As an application we show that the five-sphere admits infinitely many families of Sasaki-Einstein metrics.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2015
- DOI:
- 10.48550/arXiv.1512.07213
- arXiv:
- arXiv:1512.07213
- Bibcode:
- 2015arXiv151207213C
- Keywords:
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- Mathematics - Differential Geometry;
- 53C25
- E-Print:
- v2: 64 pages, added proof of converse of main result