Stability of Sasaki-extremal metrics under complex deformations

Abstract

We consider the stability of Sasaki-extremal metrics under deformations of the complex structure on the Reeb foliation. Given such a deformation preserving the action of a compact subgroup of the automorphism group of a Sasaki-extremal structure, a sufficient condition is given involving the nondegeneracy of the relative Futaki invariant for the deformations to contain Sasaki-extremal structures. Deformations of Sasaki-Einstein metrics are also considered, where it suffices that the deformation preserve a maximal torus. As an application, new families of Sasaki-Einstein and Sasaki-extremal metrics are given on deformations of well known 3-Sasaki 7-manifolds.

Added the obstruction to the existence of Sasaki structures under transversal complex deformations. 30 pages and 1 figure

References in corpus (3)

• Sasaki-Einstein Manifolds and Volume Minimisation
• Canonical Sasakian Metrics
• Sasaki-Einstein 5-manifolds associated to toric 3-Sasaki manifolds

Cited by in corpus (4)

• Equivariant localization and holography
• Deformations of constant scalar curvature Sasakian metrics and K-stability
• Branes wrapped on quadrilaterals
• The local moduli of Sasaki-Einstein rational homology 7-spheres and invertible polynomials