Weakly 1-completeness of holomorphic fiber bundles over compact Kähler manifolds

Abstract: In 1985 Diederich and Ohsawa proved that every disc bundle over a compact K\"ahler manifold is weakly 1-complete. In this paper, under certain conditions we generalize this result to the case of fiber bundles over compact K\"ahler manifolds whose fibers are bounded symmetric domains. Moreover if the bundle is obtained by the diagonal action on the product of irreducible bounded symmetric domains, we show that it is hyperconvex.