%0 Journal Article %T Vector Bundles on non-K£¿hler elliptic principal bundles %A Vasile Brinzanescu %A Andrei D. Halanay %A G¨¹nther Trautmann %J Mathematics %D 2010 %I arXiv %X We study relatively semi-stable vector bundles and their moduli on non-K\"ahler principal elliptic bundles over compact complex manifolds of arbitrary dimension. The main technical tools used are the twisted Fourier-Mukai transform and a spectral cover construction. For the important example of such principal bundles, the numerical invariants of a 3-dimensional non-K\"ahler elliptic principal bundle over a primary Kodaira surface are computed. %U http://arxiv.org/abs/1008.3365v7