  Main Theorem (3.3): Let $M$ be a compact four-dimensional manifold either
with curvature, positive on complex isotropic two-planes, or self-dual of
positive scalar curvature. If $\pi_1 (M)$ admits a nontrivial unitary
representation, and $M$ is orientable, then there exists a surjective
homomorphism from $\pi_1 (M)$ on $\bbz$.
  Corollary: If $\pi_1 (M)$ is finite, then either $\pi_1 (M) = 1$, or $\pi_1
(M) = \bbz_2$.
  Observe that finitely presented groups which do not admit a nontrivial
unitary representation, are extremely rare (see 3.4).
