2009/11/30 by H. Lü, H. Lu, Yi Pang +1 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Calabi–Yau manifold #Differential geometry #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic function #Mathematical analysis #Mathematical physics #Mathematics #Metric (unit) #Orbifold #Physics #Pure mathematics #Singularity #gr-qc #hep-th #math.DG
paper · pdf · doi:10.1088/0264-9381/27/15/155018
published in Classical and Quantum Gravity 27(15), 155018 (IOP Publishing) · 29 pages, no figures, version appeared in Classical and Quantum Gravity
openalex publication_date 2010/06/24 · arxiv created 2010/07/15 · arxiv updated 2010/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Recently, a metric construction for the Calabi-Yau 3-folds from a four-dimensional hyperkahler space by adding a complex line bundle was proposed. We extend the construction by adding a U(1) factor to the holomorphic (3,0)-form, and obtain the explicit formalism for a generic hyperkahler base. We find that a discrete choice arises: the U(1) factor can either depend solely on the fibre coordinates or vanish. In each case, the metric is determined by one differential equation for the modified Kahler potential. As explicit examples, we obtain the generalized resolutions (up to orbifold singularity) of the cone of the Einstein-Sasaki spaces Yp,q. We also obtain a large class of new singular CY3 metrics with SU(2)× U(1) or SU(2)× U(1)2 isometries.