Positive Self Dual Einstein Orbifolds with One-Dimensional Isometry Group

2007/03/24 by Luca Bisconti, Bisconti, Luca
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG

paper · pdf · doi:10.48550/arxiv.math/0703721

117 pages

arxiv created 2007/03/24 · openalex publication_date 2007/03/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The aim of this thesis is to construct new examples of compact orbifolds O⁴(Θ) which admit a self dual Einstein (SDE) metric of positive scalar curvature s>0, with a one-dimensional group of isometries. In particular we want to prove that these examples are different from those described by Boyer, Galicki and Piccinni in 3-Sasakian geometry, nilpotents orbits, and exeptional quotients. We construct explicitly our new examples as quaternion-Kahler reductions of the quaternion Kahler Grassmannian Gr₄(ℝ⁸) by an isometric action of a 3-torus T³_Θ⊂ T⁴⊂ SO(8) ⊂ Sp(8) on the sphere S³¹⊂ ℍ⁸, where Θ is an interger 3× 4 weight matrix.

Citations

• Calibrated geometries

Related

• Examples of Self-dual, Einstein metrics of (2,2)-signature
• 3-Sasakian Geometry, Nilpotent Orbits, and Exceptional Quotients
• Scalar-flat Kähler orbifolds via quaternionic-complex reduction
• Self-dual Einstein Hermitian four manifolds
• Non-compact Einstein manifolds with unimodular isometry group