Complex manifolds with generating tangent bundles

preprint2012arXivOpen access

Abstract

Let MM be a close complex manifold and TMTM its holomorphic tangent bundle. We prove that if the global holomorphic sections of tangent bundle generate each fibre, then MM is a complex homogeneous manifold. Our proof depends on the complex version of Chow-Rashevskii theorem in Carnot-Caratheodory spaces.

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