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arXiv · 1312.3686

Deformations of constant scalar curvature Sasakian metrics and K-stability

Carl Tipler·Craig van Coevering
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Abstract

Extending the work of G. Székelyhidi and T. Brönnle to Sasakian manifolds we prove that a small deformation of the complex structure of the cone of a constant scalar curvature Sasakian manifold admits a constant scalar curvature structure if it is K-polystable. This also implies that a small deformation of the complex structure of the cone of a constant scalar curvature structure is K-semistable. As applications we give examples of constant scalar curvature Sasakian manifolds which are deformations of toric examples, and we also show that if a 3-Sasakian manifold admits a non-trivial transversal complex deformation then it admits a non-trivial Sasaki-Einstein deformation.

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Carl Tipler, Craig van Coevering. 2015-01-18. Deformations of constant scalar curvature Sasakian metrics and K-stability. https://doi.org/10.1093/imrn%2Frnv029

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