On Sasaki-Ricci solitons and their deformations

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 generalized Sasaki-Ricci solitons, generalizing results of Li in the Kähler setting and of He and Sun by relaxing some of their assumptions. © 2016 by Walter de Gruyter