Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 052-02. Integrability of split tangent bundles on rationally connected manifolds
Manuscript map · lines 3545–3554
OpenAI@2026-10-07#rem:oai-p-052-02
Authors: OpenAI. Family 052.
Title: Integrability of split tangent bundles on rationally connected manifolds.
Abstract: 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.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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