A construction of Poincaré-Einstein metrics of cohomogeneity one on the ball

2018/05/11 by Y. Matsumoto, Matsumoto, Yoshihiko · 1 citation
Mathematics · Physics and Astronomy · #53C25 (Primary) 53A30 (Secondary) #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.1805.04505

openalex publication_date 2018/05/11 · openalex created_date 2018/05/17 · openalex updated_date 2026/07/28

Abstract

We exhibit an explicit one-parameter smooth family of Poincaré-Einstein metrics on the even-dimensional unit ball whose conformal infinities are the Berger spheres. Our construction is based on a Gibbons-Hawking-type ansätz of Page and Pope. The family contains the hyperbolic metric, converges to the complex hyperbolic metric at one of the ends, and at the other end the ball equipped with our metric collapses to a Poincaré-Einstein manifold of one lower dimension with an isolated conical singularity.

Citations

• Some remarks on conic degeneration and bending of Poincaré-Einstein metrics
• On Uniqueness of Conformally Compact Einstein Metrics with Homogeneous Conformal Infinity
• On Uniqueness And Existence of Conformally Compact Einstein Metrics with Homogeneous Conformal Infinity. II

Cited by

• Deformations and Einstein metrics I

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