Inserted: 14 may 2016
Last Updated: 4 jul 2017
Journal: arXiv:1605.03368 [math.DG]
We study cohomological properties of complex manifolds. In particular, under suitable metric conditions, we extend to higher dimensions a result by A. Teleman , wich provides an upper bound for the Bott-Chern cohomology in terms of Betti numbers for compact complex surfaces according to the dichotomy $b_1$ even or odd.