Title: Non-Abelian Seiberg-Witten equations on Einstein manifolds.


Abstract:

	We prove that if the non-Abelian Seiberg-Witten equation on the positive spinor bundle
has a solution over a Einstein four manifolds X, then X has a U(2,2) anti-self-dual projective 
connection and X has non-positive signature. 

	When the signature equals zero, Using holonomy arguments, we show that the universal 
covering of X must be the Euclidean space, the product of disks or the four ball.