a short question: Is every 3Sasakian manifold a SasakiEinstein manifold? If not, do you have an example? If yes, how can I prove this?
Thanks and best regards
a short question: Is every 3Sasakian manifold a SasakiEinstein manifold? If not, do you have an example? If yes, how can I prove this? Thanks and best regards 


Yes, because a manifold is SasakiEinstein if and only if its metric cone is Ricciflat Kähler, whereas the cone of a 3sasakian manifold is hyperkähler. See, for instance, Bär's "Real Killing spinors and holonomy" published in CMP. 

