Rigidité d'Einstein du plan hyperbolique complexe

Details Rigidité d'Einstein du plan hyperbolique complexe Rigidité d'Einstein du plan hyperbolique complexe

2001-12-11

arxiv.org/abs/math/0112099v3

J. reine angew. Math. 567 (2004) 175-213

Mathematics

Differential Geometry

31 pages, french text, some typos corrected. Proof of the result announced in CR. Acad. Sci. Paris. Ser. I 334 (2002) 671-676

Scientific paper

We prove that every Einstein metric on the unit ball B^4 of C^2, asymptotic to the Bergman metric, is equal to it up to a diffeomorphism. We need a solution of Seiberg--Witten equations in this infinite volume setting. Therefore, and more generally, if M^4 is a manifold with a CR-boundary at infinity, an adapted spinc-structure which has a non zero Kronheimer--Mrowka invariant and an asymptotically complex hyperbolic Einstein metric, we produce a solution of Seiberg--Witten equations with an strong exponential decay property.

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