Sasaki-Einstein space T 1,1 , transverse Kähler-Ricci flow and Sasaki-Ricci soliton

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