a short question: Is every 3-Sasakian manifold a Sasaki-Einstein manifold? If not, do you have an example? If yes, how can I prove this?


Thanks and best regards



Is every 3-Sasakian a Sasakian-Einstein manifold?
Yes, because a manifold is Sasaki-Einstein if and only if its metric cone is Ricci-flat Kähler, whereas the cone of a 3-sasakian manifold is hyperkähler.


See, for instance, Bär's "[Real Killing spinors and holonomy](https://doi.org/10.1007/BF02102106)" published in CMP.


