SOME REMARKS ON ALMOST AND STABLE ALMOST COMPLEX-MANIFOLDS

In the first part we give necessary and sufficient conditions for the existence of a stable almost complex structure on a 10-manifold M with H-1(M;Z) = 0 and no 2-torsion in H-i(M;Z) for i = 2, 3. Using the Cla ssification Theorem of Donaldson we give a reformulation of the condit ions for a 4-manifold to be almost complex in terms of Betti numbers a nd the dimension of the +/--eigenspaces of the intersection form. In t he second part we give general conditions for an almost complex manifo ld to admit infinitely many almost complex structures and apply these to symplectic manifolds, to homogeneous spaces and to complete interse ctions.