2006/05/03 by Georgi Ganchev, Vesselka Mihova · 1 citation
Mathematics · Medicine · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Pelvic and Acetabular Injuries #math.DG #msc:53B35 #msc:53C25
paper · pdf · doi:10.1016/j.geomphys.2008.02.002
published as Journal of Geometry and Physics, 58 (2008), 7, 803-824. · 28
arxiv created 2006/05/03 · openalex publication_date 2008/02/11 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Using as an underlying manifold an alpha-Sasakian manifold we introduce warped product Kaehler manifolds. We prove that if the underlying manifold is an alpha-Sasakian space form, then the corresponding Kaehler manifold is of quasi-constant holomorphic sectional curvatures with special distribution. Conversely, we prove that any Kaehler manifold of quasi-constant holomorphic sectional curvatures with special distribution locally has the structure of a warped product Kaehler manifold whose base is an alpha-Sasakian space form. Considering the scalar distribution generated by the scalar curvature of a Kaehler manifold, we give a new approach to the local theory of Bochner-Kaehler manifolds. We study the class of Bochner-Kaehler manifolds whose scalar distribution is of special type. Taking into account that any manifold of this class locally is a warped product Kaehler manifold, we describe all warped product Bochner-Kaehler metrics. We find four families of complete metrics of this type.