The Einstein-Hilbert Functional and the Sasaki-Futaki Invariant

作者：Boyer Charles P; Huang Hongnian; Legendre Eveline^*; Tonnesen Friedman Christina W

来源：International Mathematics Research Notices, 2017, (7): 1942-1974.

DOI：10.1093/imrn/rnw076

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.

• 出版日期2017-4