Sasaki–Einstein metrics and K–stability
Copyright policy )Sasaki–Einstein metrics and K–stability
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.
Comment: v2: 64 pages, added proof of converse of main result
- University of Notre Dame United States
- Harvard University United States
- Massachusetts Institute of Technology United States
Mathematics - Differential Geometry, Kähler-Einstein manifolds, Sasaki, K-stability, 53C25, Kähler–Einstein, Sasaki metric, Special Riemannian manifolds (Einstein, Sasakian, etc.), Kähler-Einstein metric, 32Q20, Notions of stability for complex manifolds, 32Q26, K–stability
Mathematics - Differential Geometry, Kähler-Einstein manifolds, Sasaki, K-stability, 53C25, Kähler–Einstein, Sasaki metric, Special Riemannian manifolds (Einstein, Sasakian, etc.), Kähler-Einstein metric, 32Q20, Notions of stability for complex manifolds, 32Q26, K–stability
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