Displaying similar documents to “Einstein manifolds, volume rigidity and Seiberg-Witten theory”

Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces

Hassan Boualem, Marc Herzlich (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Any Kähler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dimension.

Selfdual Einstein hermitian four-manifolds

Vestislav Apostolov, Paul Gauduchon (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We provide a local classification of selfdual Einstein riemannian four-manifolds admitting a positively oriented hermitian structure and characterize those which carry a hyperhermitian, non-hyperkähler structure compatible with the negative orientation. We show that selfdual Einstein 4-manifolds obtained as quaternionic quotients of P 2 and H 2 are hermitian.