Abstract
A CY bundle on a connected compact complex manifold X was a crucial ingredient in constructing differential systems for period integrals in an earlier paper by Lian and Yau, by lifting line bundles from the base X to the total space. A question was therefore raised as to whether there exists such a bundle that supports the liftings of all line bundles from X, simultaneously. This was a key step for giving a uniform construction of differential systems for arbitrary complete intersections in X. In this paper, we answer the existence question in the affirmative if X is assumed to be Kohler, and also in general if the Picard group of X is assumed to be discrete. Furthermore, we prove a rigidity property of CY bundles if the principal group is an algebraic torus, showing that such a CY bundle is essentially determined by its character map.