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Article Dans Une Revue Int.Math.Res.Not. Année : 2017

The Einstein–Hilbert Functional and the Sasaki–Futaki Invariant

Charles P. Boyer
  • Fonction : Auteur
Hongnian Huang
  • Fonction : Auteur

Résumé

We show that the Einstein–Hilbert functional, as a functional on the space of Reeb vector fields, detects the vanishing Sasaki–Futaki invariant. In particular, this provides an obstruction to the existence of a constant scalar curvature Sasakian metric. As an application we prove that K-semistable polarized Sasaki manifold has vanishing Sasaki–Futaki invariant. We then apply this result to show that under the right conditions on the Sasaki join manifolds of [6], a polarized Sasaki manifold admits constant scalar curvature Sasaki metric if it is K-polystable.

Dates et versions

hal-01553892 , version 1 (03-07-2017)

Identifiants

Citer

Charles P. Boyer, Hongnian Huang, Eveline Legendre, Christina W. Tønnesen-Friedman. The Einstein–Hilbert Functional and the Sasaki–Futaki Invariant. Int.Math.Res.Not., 2017, 2017 (7), pp.1942-1974. ⟨10.1093/imrn/rnw076⟩. ⟨hal-01553892⟩
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