Cohomology of bundles on homological Hopf manifold
  We discuss the properties of complex manifolds having rational homology of $S^1 \times S^{2n-1}$ including those constructed by Hopf, Kodaira and Brieskorn-van de Ven. We extend certain previously known vanishing properties of cohomology of bundles on such manifolds.As an application we consider degeneration of Hodge-deRham spectral sequence in this non Kahler setting. 
A.Libgober