TITLE: Example of Non-Conformally Flat Einstein Manifold?
QUESTION [6 upvotes]: Does there exist an Einstein manifold which is not conformally flat, which is to say one which has non-vanishing Weyl tensor. If so, what is a good example.

REPLY [3 votes]: By the standard curvature decomposition, for an Einstein metric, if the Weyl curvature vanishes, then the sectional curvature is constant, so other than space forms, all Einstein manifolds are not conformally flat.
Sorry I didn't see Deane Yang's answer, he already got this answer.