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dg.differential geometry – Regarding projective manifolds with decomposable actual tangent bundle Answer

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dg.differential geometry – Regarding projective manifolds with decomposable actual tangent bundle

Let $X$ breathe a complicated projective manifold. Suppose its actual tangent bundle $T_{mathbb{R}}X$ splits as a direct sum of two sub-bundles of plane diploma. Does this give any helpful details about the manifold $X$ (e.g. its Euler attribute, and so on.)?

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