2023/12/03 by Indranil Biswas, Biswas, Indranil, Sorin Dumitrescu +1
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
paper · pdf · doi:10.48550/arxiv.2312.01399
openalex publication_date 2023/12/03 · openalex created_date 2023/12/06 · openalex updated_date 2026/07/28
We prove that any holomorphic vector bundle admitting a holomorphic connection, over a compact Kähler Calabi-Yau manifold, also admits a flat holomorphic connection. This addresses a particular case of a question asked by Atiyah and generalizes a result previously obtained in \citeBD for simply connected compact Kähler Calabi-Yau manifolds. We give some applications of it in the framework of Cartan geometries and foliated Cartan geometries on Kähler Calabi-Yau manifolds.