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

Weakly 1-completeness of holomorphic fiber bundles over compact K\"ahler manifolds