Einstein Metrics on Spheres

Details Einstein Metrics on Spheres Einstein Metrics on Spheres

2003-09-24

arxiv.org/abs/math/0309408v2

Annals of Mathematics 162(1) (2005), 557-580.

Mathematics

Differential Geometry

19 pages, some references added and clarifications made. to appear in Annals of Mathematics

Scientific paper

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.

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