EXAMPLES OF COMPACT NEGATIVELY CURVED ALMOST COMPLEX, BUT NOT COMPLEX, MANIFOLDS

Abstract

In this paper, we provide infinitely many examples of compact negatively curved almost complex, but not complex, manifolds of complex dimension 2n + 1 or 2n + 2 by using strongly pseudoconvex homogeneous domains in an almost complex manifold. Unlike the Kodaira–Thurston manifold which is the flat case, the first Betti number of the constructed manifolds is even, and their first homology group is, in fact, isomorphic to ℤ4n+2 or ℤ4n+4.