  In this paper, we prove a classification theorem of 4-manifolds according to
some conformal invariants, which generalizes the conformally invariant sphere
theorem of Chang-Gursky-Yang \cite{CGY}. Moreover, it provides a
four-dimensional analogue of the well-known classification theorem of
Schoen-Yau \cite{SY2} on 3-manifolds with positive Yamabe invariants.
