Complex manifolds with generating tangent bundles

2008/08/20 by Renyi Ma, Ma, Renyi
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.DG

paper · pdf · doi:10.48550/arxiv.0808.2690

openalex publication_date 2008/08/20 · arxiv created 2012/03/15 · arxiv updated 2012/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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