Curves on Endo–Pajitnov Manifolds

Endo–Pajitnov manifolds are generalizations to higher dimensions of the Inoue surfaces $S^M$. We study the existence of complex submanifolds in Endo–Pajitnov manifolds. We identify a class of these manifolds that do contain compact complex submanifolds and establish an algebraic condition under which an Endo–Pajitnov manifold contains no compact complex curves.