Hi, can you give me a good paper (in the sense of a simple introduction) about SasakiEinstein manifolds?
Thank you and best regards Florian M.
Hi, can you give me a good paper (in the sense of a simple introduction) about SasakiEinstein manifolds? Thank you and best regards Florian M. 


Well, now there is a great textbook for SasakiEinstein geometry, by BoyerGalicki: Here is a link to the book at Oxford University Press I would definitely start there. 


I agree with Spiro's recommendation to pick up the book by Boyer and Galicki, but I would like to add the following. There are at least two ways to get to SasakiEinstein manifolds. The traditional approach is to consider them as special cases of contact manifolds and I believe that this is the point of departure, or at least the main thrust of the above book. But another way, and in my case the way I first met them, is via their characterisation as those manifolds whose metric cone is CalabiYau, which is particularly transparent in the context of spin geometry. Said differently, a CalabiYau manifold admits parallel spinor fields, and this means that a SasakiEinstein manifold admits real Killing spinor fields. The relation between the two, as well as the uniform way of recovering the contact structure and associated Sasakian paraphernalia from the Killing spinors, is explained in the beautiful and short paper of Christian Bär's Real Killing spinors and holonomy, which itself can be thought of as a lucid introduction to this aspect of SasakiEinstein manifolds. 

