Level 2: Integrability of split tangent bundles on rationally connected manifolds

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LEVEL 2 OF 2 · Tangent-bundle splittings and universal covers

Integrability of split tangent bundles on rationally connected manifolds

expertly designed by an internal OpenAI model · released 2026-09-23 · original PDF

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How to play: We prove that both summands of every specified holomorphic splitting of the tangent bundle of a smooth rationally connected projective complex manifold into two positive-rank subbundles are integrable. This proves Höring's conjecture on rationally connected projective manifolds. Höring's product theorem then gives a product decomposition compatible with the specified splitting.

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