Sasaki-Einstein space T1,1, transverse Kahler-Ricci flow and Sasaki-Ricci soliton

We examine the compact Sasaki manifolds in view of transverse Kahler geometry and transverse Kahler-Ricci flow. In particular we study the transverse Kahler geometry of the five-dimensional Sasaki-Einstein space T-1,T-1. For this purpose a set of local holomorphic coordinates is introduced and a Sasakian analogue of the Kahler potential is produced. There are considered deformations of the contact structure fixing the Reeb foliation while varying the Kahler metric on the transverse holomorphic structure.