Non-existence of cohomogeneity one Einstein metrics of two summands

2025/05/10 by Hanci Chi, Chi, Hanci
Mathematics · Physics and Astronomy · #53C25 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2505.06631

openalex publication_date 2025/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the non-existence of cohomogeneity one Einstein metrics on a class of compact manifolds arising as double disk bundles, whose principal orbits split into two inequivalent irreducible summands. The proof uses a phase space barrier argument that yields a new obstruction to the existence of closed cohomogeneity one Einstein metrics, even when the principal orbits admit homogeneous Einstein metrics.

Citations

• Existence of cohomogeneity one Einstein metrics
• K-stability and Kähler-Einstein metrics

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