Geometry & Topology

Sasaki–Einstein metrics and K–stability

Tristan C Collins and Gábor Székelyhidi

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We show that a polarized affine variety with an isolated singularity admits a Ricci flat Kähler cone metric if and only if it is K–stable. This generalizes the Chen–Donaldson–Sun 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.

Article information

Geom. Topol., Volume 23, Number 3 (2019), 1339-1413.

Received: 25 September 2017
Revised: 11 July 2018
Accepted: 8 August 2018
First available in Project Euclid: 5 June 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32Q20: Kähler-Einstein manifolds [See also 53Cxx] 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Secondary: 32Q26: Notions of stability

K–stability Kähler–Einstein Sasaki


Collins, Tristan C; Székelyhidi, Gábor. Sasaki–Einstein metrics and K–stability. Geom. Topol. 23 (2019), no. 3, 1339--1413. doi:10.2140/gt.2019.23.1339.

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