%0 Journal Article
%T Deformations of constant scalar curvature Sasakian metrics and K-stability
%A Carl Tipler
%A Craig van Coevering
%J Mathematics
%D 2013
%I arXiv
%R 10.1093/imrn/rnv029
%X Extending the work of G. Sz\'ekelyhidi and T. Br\"onnle 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.
%U http://arxiv.org/abs/1312.3686v3