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Coelho, R.; Kotschick, D. (2020): Lifts of projective bundles and applications to string manifolds. In: Bulletin of the London Mathematical Society, Vol. 53, No. 2: pp. 470-481
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We discuss the problem of lifting projective bundles to vector bundles, giving necessary and sufficient conditions for a lift to exist both in the smooth and in the holomorphic categories. These criteria are formulated and proved in the language of topology and complex differential geometry, respectively. We also prove some results about Kahler structures on string six-manifolds. For manifolds without any odd-degree cohomology, one conclusion is that all such Kahler structures are projective and of negative Kodaira dimension.