A construction of Poincaré–Einstein metrics of cohomogeneity one on the ball
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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.References
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Additional Information
- Yoshihiko Matsumoto
- Affiliation: Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan; Department of Mathematics, Stanford University, Stanford, California 94305-2125
- MR Author ID: 1025212
- Email: matsumoto@math.sci.osaka-u.ac.jp
- Received by editor(s): October 29, 2018
- Received by editor(s) in revised form: December 30, 2018
- Published electronically: May 1, 2019
- Additional Notes: This work was partially supported by JSPS KAKENHI Grant Number JP17K14189 and JSPS Overseas Research Fellowship.
- Communicated by: Jia-Ping Wang
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3983-3993
- MSC (2010): Primary 53C25; Secondary 53A30
- DOI: https://doi.org/10.1090/proc/14525
- MathSciNet review: 3993790