New examples of Sasaki-Einstein manifolds

2011/03/29 by Toshiki Mabuchi, Mabuchi, Toshiki, Yasuhiro Nakagawa +1 · 1 citation
Mathematics · #2010: Primary 53C25 #53C55 #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Secondary 32Q20

paper · pdf · doi:10.48550/arxiv.1103.5573

openalex publication_date 2011/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, stimulated by the existence result of Futaki-Ono-Wang for toric Sasaki-Einstein metrics, we obtain new examples of Sasaki-Einstein metrics on S¹-bundles associated to canonical line bundles of P¹-bundles over Kähler-Einstein Fano manifolds, even though the Futaki's obstruction does not vanish. Here the method of Sakane and Koiso is used, and our examples include non-toric Sasaki-Einstein manifolds.

Cited by

• On Sun-Zhang's theory of Fano fibrations -- weighted volumes, moduli and bubbling Fano fibrations

Related

• New Results in Sasaki-Einstein Geometry
• Examples of Einstein manifolds in odd dimensions
• The Sasaki Join, Hamiltonian 2-forms, and Sasaki-Einstein Metrics
• New Einstein Metrics in Dimension Five
• Kahler geometry on toric manifolds, and some other manifolds with large symmetry