Einstein metrics on spheres
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Publication:816333
DOI10.4007/ANNALS.2005.162.557zbMATH Open1093.53044arXivmath/0309408OpenAlexW2105851846WikidataQ30051682 ScholiaQ30051682MaRDI QIDQ816333
Author name not available (Why is that?)
Publication date: 10 March 2006
Published in: (Search for Journal in Brave)
Abstract: We prove the existence of an abundance of new Einstein metrics on odd dimensional spheres including exotic spheres, many of them depending on continuous parameters. The number of families as well as the number of parameter grows double exponentially with the dimension. Our method of proof uses Brieskorn-Pham singularities to realize spheres (and exotic spheres) as circle orbi-bundles over complex algebraic orbifolds, and lift a Kaehler-Einstein metric from the orbifold to a Sasakian-Einstein metric on the sphere.
Full work available at URL: https://arxiv.org/abs/math/0309408
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