2015/09/18 by Aleksei Golota, Golota, Aleksei
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.1509.05787
openalex publication_date 2015/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A locally conformally Kähler (LCK) manifold is a complex manifold whose universal cover is Kähler with monodromy group acting on the universal cover by holomorphic homotheties. A Vaisman manifold M is a compact non-Kähler LCK manifold admitting an action of a holomorphic conformal flow lifting to an action on a Kähler cover by nontrivial homotheties. When the orbits of the action on M are compact, it is known that every stable holomorphic vector bundle over M, dim(M) ≥ 3, is equivariant and filtrable. In the present paper we generalize this result to irregular Vaisman manifolds.