Abstract
We extend to the Sasakian setting a result of Tian and Zhu about the decomposition of the Lie algebra of holomorphic vector fields on a Kähler manifold in the presence of a Kähler-Ricci soliton. Furthermore we apply known deformations of Sasakian structures to a Sasaki-Ricci soliton to obtain a stability result concerning \emph{generalized} Sasaki-Ricci solitons, generalizing Li in the Kähler setting and also He and Song by relaxing some of their assumptions.
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