Symplectic obstructions to the existence of $\omega$-compatible Einstein metrics

Abstract

It is shown that the existence of an $\omega$-compatible Einstein metric on a compact symplectic manifold $(M,\omega )$ imposes certain restrictions on the symplectic Chern numbers. Examples of symplectic manifolds which do not satisfy these restrictions are given. The results offer partial support to a conjecture of Goldberg.

11 pages