Symplectic obstructions to the existence of ω-compatible Einstein metrics

2003/10/09 by Tedi Draghici, Tedi Drăghici, Draghici, Tedi
Mathematics · #53C25 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG #msc:53C25

paper · pdf · doi:10.48550/arxiv.math/0310126

11 pages

arxiv created 2003/10/09 · openalex publication_date 2003/10/09 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

It is shown that the existence of an ω-compatible Einstein metric on a compact symplectic manifold (M,ω) imposes certain restrictions on the symplectic Chern numbers. Examples of symplectic manifolds which do not satisfy these restrictions are given. The results offer partial support to a conjecture of Goldberg.

Related

• Einstein Metrics, Symplectic Minimality, and Pseudo-Holomorphic Curves
• Einstein Manifolds and Extremal Kahler Metrics
• The symplectic Hadamard question
• Nonexistence for complete Kähler Einstein metrics on some noncompact manifolds
• Cosymplectic Chern--Hamilton conjecture