2024/04/28 by Debjit Pal, Pal, Debjit, Mainak Poddar +1
Mathematics · #32L05 #32L20. Secondary: 57R22 #53D05 #57R30 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Primary: 53D18 #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.2404.18113
openalex publication_date 2024/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the notion of a strong generalized holomorphic (SGH) fiber bundle and develop connection and curvature theory for an SGH principal G-bundle over a regular generalized complex (GC) manifold, where G is a complex Lie group. We develop a de Rham cohomology for regular GC manifolds, and a Dolbeault cohomology for SGH vector bundles. Moreover, we establish a Chern-Weil theory for SGH principal G-bundles under certain mild assumptions on the leaf space of the GC structure. We also present a Hodge theory along with associated dualities and vanishing theorems for SGH vector bundles. Several examples of SGH fiber bundles are given.