2 problems

Let $X$ be a projective manifold with a splitting … Assume that $X$ is rationally connected. Integrability conjecture. The subbundles $V_1$ and $V_2$ are integrable. The conjecture…

Let $\mathsf{X}$ be a compact Kähler manifold equipped with a holomorphic decomposition … of the tangent bundle such that each subbundle $\bigoplus_{j\in J} \mathcal{F}_j$, for…