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Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces. (English) Zbl 1170.53308

Summary: 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.

MSC:

53C24 Rigidity results
53C27 Spin and Spin\({}^c\) geometry
53C55 Global differential geometry of Hermitian and Kählerian manifolds
58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
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References:

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