Stability of Sasaki-extremal metrics under complex deformations

Details Stability of Sasaki-extremal metrics under complex deformations Stability of Sasaki-extremal metrics under complex deformations

2012-04-07

arxiv.org/abs/1204.1630v1

Mathematics

Differential Geometry

29 pages, 1 figure

Scientific paper

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.

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