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 Li in the Kähler setting and also He and Song by relaxing some of their assumptions.2010 Mathematics Subject Classification. 53C25.

Sasakian immersions of Sasaki-Ricci solitons into Sasakian space forms

“…These have been introduced in [10] as special solutions of the Sasaki-Ricci flow of [18]. Since then SRS have received growing interest, see for instance [16,19].…”

“…The equation ( 5) is commonly used in literature to define Sasaki-Ricci solitons, see for instance [16,19]. On the other hand, on a complex manifold M a Kähler-Ricci soliton (KRS for short) is defined to be a pair (g, X) where g is a Kähler metric and X is a holomorphic vector field on M satisfying ( 6)…”

On Calabi extremal Kähler-Ricci solitons

“…Indeed there are Sasakian analogues of Theorem 4 done by Boyer and Galicki and an extension of Theorem 1.7 done by the second author in [18]. Moreover, the Lichnerowicz equations hold as well for the transverse quantities, see again [4].…”