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arxiv: 0808.2690 · v4 · pith:CCXAIO76new · submitted 2008-08-20 · 🧮 math.AG · math.DG

Complex manifolds with generating tangent bundles

classification 🧮 math.AG math.DG
keywords complextangentbundleholomorphicmanifoldbundlescarnot-caratheodorychow-rashevskii
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Let $M$ be a close complex manifold and $TM$ its holomorphic tangent bundle. We prove that if the global holomorphic sections of tangent bundle generate each fibre, then $M$ is a complex homogeneous manifold. Our proof depends on the complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces.

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