On Eta-Einstein Sasakian Geometry

2004/06/30 by Charles P. Boyer, Krzysztof Galicki, Paola Matzeu · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Computer science #Context (archaeology) #Einstein #Foliation (geology) #Geology #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Holonomy #Manifold (fluid mechanics) #Mathematical physics #Mathematics #Metric (unit) #Orbifold #Physics #Pure mathematics #Space (punctuation) #hep-th #math.DG

paper · pdf · doi:10.1007/s00220-005-1459-6

published as Commun.Math.Phys.262:177-208,2006 · 31 pages, minor changes made, to appear in Commun. Math. Phys

arxiv created 2005/10/31 · openalex publication_date 2005/11/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study eta-Einstein geometry as a class of distinguished Riemannian metrics on contact metric manifolds. In particular, we use a previous solution of the Calabi problem for Sasakian geometry to prove the existence of eta-Einstein structures on many different compact manifolds, including exotic spheres. We also relate these results to the existence of Einstein-Weyl structures.

Citations

• Nonlinear Analysis on Manifolds. Monge-Ampère Equations
• Principles of Algebraic Geometry
• Riemannian Geometry of Contact and Symplectic Manifolds
• Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals
• The Geometries of 3-Manifolds
• Beispiele zur Differentialtopologie von Singularit�ten
• On the ricci curvature of a compact kähler manifold and the complex monge‐ampére equation, I
• Einstein metrics on spheres
• The local moduli ofSasakian 3‐manifolds
• Einstein metrics on 5-dimensional Seifert bundles

Cited by

• Supersymmetric Warped Solutions from Type IIB Orientifold Reduction
• Canonical Sasakian Metrics