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arXiv · 1512.07213

Sasaki-Einstein metrics and K-stability

Tristan C. Collins·Gábor Székelyhidi
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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.

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Tristan C. Collins, Gábor Székelyhidi. 2017-09-24. Sasaki-Einstein metrics and K-stability. https://doi.org/10.2140/gt.2019.23.1339

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