2018/11/27 by Teng Huang, Huang, Teng
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Bounded function #Bundle #Clifford bundle #Connection (principal bundle) #Curvature #Differential Geometry (math.DG) #FOS: Mathematics #Frame bundle #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Hermitian manifold #Hermitian matrix #Hyperkähler manifold #Kähler manifold #Manifold (fluid mechanics) #Materials science #Mathematical analysis #Mathematical physics #Mathematics #Normal bundle #Omega #Physics #Pure mathematics #Quantum mechanics #Ricci curvature #Ricci-flat manifold #Vector bundle #math.DG
paper · pdf · open access · doi:10.48550/arxiv.1811.10772
published in arXiv (Cornell University) (Cornell University) · We would like to thank the anonymous referee pointed out that we can study the nonvanishing theorem in the small enough $L^{\infty}$-norm case. To appear in Isr. J. Math
openalex publication_date 2018/11/27 · arxiv created 2019/07/22 · arxiv updated 2019/07/23 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
Let E be a Hermitian vector bundle over a complete Kähler manifold (X,ω), dimℂX=n, with a d(bounded) Kähler form ω, dA be a Hermitian connection on E. The goal of this article is to study the L2-Hodge theory on the vector bundle E. We extend the results of Gromov's \citeGro to the Hermitian vector bundle. At last, as an application, we prove a gap result for Yang-Mills connection on the bundle E over X.